Copyright by Priti Duggal 2006 · Priti Duggal, MSE The University of Texas at Austin, 2006...

Copyright

by

Priti Duggal

2006

An Experimental Study of Rim Formation in Single-Shot

Femtosecond Laser Ablation of Borosilicate Glass

by

Priti Duggal, B.Tech.

Thesis

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science in Engineering

The University of Texas at Austin

August 2006



Approved by

Supervising Committee:

Adela Ben-Yakar

John R. Howell

Acknowledgments

My sincere thanks to my advisor Dr. Adela Ben-Yakar for showing trust in me

and for introducing me to the exciting world of optics and lasers. Through numerous

valuable discussions and arguments, she has helped me develop a scientific

approach towards my work. I am ready to apply this attitude to my future projects

and in other aspects of my life.

I would like to express gratitude towards my reader, Dr. Howell, who gave me

very helpful feedback at such short notice.

My lab-mates have all positively contributed to my thesis in ways more than

one. I especially thank Dan and Frederic for spending time to review the initial drafts

of my writing.

Thanks to Navdeep for giving me a direction in life. I am excited about the

future!

And, most importantly, I want to thank my parents. I am the person I am,

because of you. Thank you.

11 August 2006

iv

Abstract



Priti Duggal, MSE

The University of Texas at Austin, 2006

Supervisor: Adela Ben-Yakar

Craters made on a dielectric surface by single femtosecond pulses often

exhibit an elevated rim surrounding the crater. In case of machining with multiple

pulses, the effect of the individual crater rims accumulates and shows up as surface

roughness in the etched microfeature. Through experiments, we investigate the

factors affecting the crater rim height and look at different methods for reducing the

rim. The ultimate intention is to develop a femtosecond micromachining technique

for etching smooth microfeatures on the surface of dielectric materials.

Experiments are carried out to study the relationship between the different

ablation crater dimensions (diameter, depth and rim height). The crater diameter is

a function of the laser fluence and the beam spot size. The fluence is varied from 5

J/cm2 to about 30 J/cm2 and the spot size is changed from 5 μm to 30 μm using

different lenses in order to change the crater width. Additionally, moving the glass

sample surface away from the focal plane of the focusing lens also alters the crater

dimensions. Measurements show a clear inverse trend between the rim height, b, to

crater depth, h, ratio and the square of the crater diameter, D, ie. b/h ∝ 1/Dx, where

x is presently unknown. As an example, an increase in crater diameter from 5 μm to

60 μm by varied means results in a decrease in the rim height/crater depth ratio

from 0.6 to 0.05 or even lesser. Craters larger than 30 μm are typically rimless.

v

Also, we conclude from our experiments that for a given pulse energy and

focusing conditions, the crater rims are observed to reduce in height by about 100 to

150 nm as the sample moves closer from the focal plane, towards the focusing lens.

Finally, we spatially reshape the Gaussian beam into a top-hat profile and

show that the beam profile affects the rim height. Ablation with the top-hat beam

profile provides relatively smaller rim heights and hence beam reshaping might be a

beneficial technique for creating low rim craters with size smaller than 10 μm.

vi

Table of Contents

1 Introduction ......................................................................................... 14 1.1 Introduction and Motivation...............................................................14 1.2 Theoretical Background ....................................................................15

1.2.1 Femtosecond Ablation in Transparent Dielectrics ...............................15 1.2.2 Accounting for Undesirable Effects ..................................................18

1.2.2.1 Non-Linear Propagation Effects – Self-focusing ............................18 1.2.2.2 Optical Aberrations..................................................................20

1.2.3 Undesirable Damage during Femtosecond Ablation Process.................20 1.2.3.1 In-Depth Discussion about the Crater Rim ..................................22

1.2.4 Possible Methods for Improving Machining Quality.............................24 1.3 Thesis Objectives.............................................................................25

2 Laser Beam Spatial Profile.................................................................... 26 2.1 Gaussian Beam Theory .....................................................................26

2.1.1 M2 Beam Propagation Factor...........................................................29 2.1.1.1 Measuring M2 factor.................................................................32

2.2 Reshaping the Gaussian Beam Profile into Top-Hat ...............................32 2.2.1 Introduction.................................................................................32 2.2.2 Theory behind Reshaping Gaussian into Top-Hat ...............................34 2.2.3 Alternative Methods for Creating a Top-Hat ......................................38

3 Ablation With Gaussian Beam Profile.................................................... 40 3.1 Design of Experiment .......................................................................40

3.1.1 Setup Details ...............................................................................41 3.1.1.1 Laser system..........................................................................41 3.1.1.2 Energy Measurement ...............................................................42 3.1.1.3 Borosilicate Glass Substrate......................................................43

3.2 Post Ablation Analysis.......................................................................43 3.3 Experimental Procedure ....................................................................44

3.3.1 Data Available..............................................................................45 3.4 Qualitative Analysis..........................................................................46 3.5 Quantitative Analysis........................................................................49

3.5.1 Crater Width, Beam Spot Size, Focal Plane Location...........................49 3.5.2 Crater Depth................................................................................56 3.5.3 Crater Rim Height.........................................................................58 3.5.4 Error Analysis ..............................................................................60

3.6 Overall Conclusions from the Entire Dataset.........................................63 4 Ablation with Top-Hat Beam Profile...................................................... 66

4.1 Experimental Setup & Procedure ........................................................66 4.1.1 Data Available..............................................................................68

4.2 Discussion about the observed trends .................................................68

vii

4.2.1 Crater Width ................................................................................68 4.2.2 Crater Depth................................................................................70 4.2.3 Crater Rim Height.........................................................................74

4.3 Comparison between ‘Gaussian’ and ‘Top-Hat’ Craters...........................76 5 Concluding Remarks ............................................................................. 82

5.1 Summary of Major Results and Conclusions .........................................82 5.1.1 Experimental Procedure.................................................................82 5.1.2 Experimental analysis....................................................................83

5.2 Recommendations for Future Work.....................................................85 6 Appendix : ............................................................................................ 86

6.1 Appendix A: M2 Measurement ............................................................86 6.2 Appendix B: Properties of Borosilicate Glass.........................................88 6.3 Appendix C: MATLAB Code Listing ......................................................89 6.4 Appendix D: Ablation With Gaussian Beam Profile.................................90 6.5 Appendix E: Ablation With Top-Hat Beam Profile...................................96

7 References: ........................................................................................ 100 8 Vita..................................................................................................... 103

viii

List of Figures

Figure 1-1: Schematic diagram of the photoionization of an electron in an atomic potential for different values of the Keldysh parameter. Tunneling Ionization is favored by strong laser field and low laser frequency. Multiphoton Ionization (MPI) is the dominant method of photoionization for high laser frequencies. [16]............................................................................................................16

Figure 1-2: Avalanche Ionization. An initially free electron linearly absorbs several laser photons through free-carrier absorption, then impact ionizes another electron [16]. .........................................................................................17

Figure 2-1: Change in beam profile and wavefront radius of curvature of Gaussian Profile with propagation distance [by courtesy of Melles Griot Inc.] .................28

Figure 2-2: Growth in beam diameter as a function of distance from the Gaussian beam waist [by courtesy of Melles Griot Inc.] ..............................................28

Figure 2-3: Embedded Gaussian beam. This case occurs quite infrequently. [by courtesy of Melles Griot]...........................................................................31

Figure 2-4: Comparison between (a) Gaussian and (b) top-hat laser beam profiles [Courtesy of Newport Corporation].............................................................34

Figure 2-5: Schematic of Experimental Setup. A circular aperture is placed in the front focal plane of the achromatic focusing lens. Both the aperture and lens are translated together towards the glass sample surface. ..................................35

Figure 2-6: Schematic of typical beam profiles in the near field (laser output), far field (at the focus of a lens), and intermediate field [37]. The sharp edge aperture forms the top-hat wave-front which becomes the object for the focusing lens. Fraunhofer diffraction pattern is seen at the focal plane and Fresnel diffraction pattern is seen away from the focal plane. ...................................36

Figure 2-7: Beam profiler images of typical beam profiles in the near field (z= ±5000 μm), far field (z= ±0 μm), intermediate field (z= ±1500 μm). The images are made with a 10X NA 0.28 objective lens, with an aperture with diameter 3 mm in its front focal plane. The incident beam is expanded from 8 mm to 22 mm before the aperture. The beam profile represents an Airy disk at z = 0, and approaches a top-hat as we move away from the focal plane..........................................38

Figure 3-1: Top-View of Experimental Setup. The focusing lens is on a translation stage and is moved towards the glass sample in controlled step-sizes during the ablation experiment. ................................................................................41

Figure 3-2: a) The focusing lens translates towards the target in all the experimental runs. Single shot ablation is carried out starting from the sample placed beyond the focal plane, till when it lies much before the focal plane. b) Sample optical images of single-shot ablation craters: E = 20 μJ, beam spot size = 6.2 μm, Gaussian beam profile, fluence ~ 16 J/cm2..................................................45

Figure 3-3: Optical image for single shot ablation crater made with f = 250 mm, E = 1000 μJ, with the glass sample beyond the focal plane of the lens. The non-uniform rim seems to be caused by the material ejected from the inner elliptical crater, and higher layer of material is deposited where there is lesser circumference available for deposition. .......................................................48

Figure 3-4: Optical images for single shot ablation craters made with f = 250 mm, E = 1000 μJ, with the glass sample at the focal plane of the lens. The rim is relatively high, and uniformly distributed around the crater boundary. ............48

ix

Figure 3-5: Optical images for single shot ablation craters made with f = 250 mm, E = 1000 μJ, with the glass sample before the focal plane of the lens. The inner rim is formed of debris and is uniform. These craters are typically rimless. ......49

Figure 3-6: Variation in crater width as the lens moves closer to the glass surface. The x-axis is normalized by the Rayleigh range. There is a dip in the trend at the focal plane, as expected. Gaussian beam profile, f = 100 mm, E = 120 μJ. Crater width is measured along a) the axis of AFM scanning, b) major axis of elliptical crater, c) minor axis of elliptical crater. For later analysis, crater widths are measured along the major axis of the ellipse, to maintain consistency.............50

Figure 3-7: Typical case of variation in ellipticity of the elliptical single shot ablations craters as the lens moves closer to the glass sample. The x-axis is normalized by the Rayleigh range. No particular trend is observed. .....................................51

Figure 3-8: Variation of Crater Width as the Glass Sample moves towards the focusing lens, f = 100 mm (Experimental Data). beam spot size at focus = 13.9 μm. The x-axis is normalized by the Rayleigh range......................................52

Figure 3-9: Expected variation in crater width with decreasing axial distance between the lens and the glass sample. This trend is seen to match with the experimental trend of Figure 3-6. .................................................................................53

Figure 3-10: Variation in (crater diameter)2 with energy for a given axial location of the glass surface with respect to the focusing lens (z/zR = -0.2). The beam spot size at each ‘z’ can be calculating by finding the slope of each curve and using equation 3-2. ..........................................................................................54

Figure 3-11: Variation in beam spot size with axial distance ‘z’ (distance between the glass surface and focusing lens). Calculated using analysis based on Figure 3-10. f = 100mm. Beam spot size at focal plane is approximately 13.9 μm...............55

Figure 3-12: Calculated Crater Depth Variation with Distance from Focal Plane. The craters are deepest at the focal plane. ........................................................56

Figure 3-13: Experimental data for variation in crater depth as the lens moves closer to the glass surface. Beam profile: Gaussian, beam spot radius = 13.9 μm, f = 100 mm. The x-axis is normalized by the Rayleigh range. .............................57

Figure 3-14: Variation in rim heights as the glass sample moves closer to the focal plane. The x-axis is normalized by the Rayleigh range. Typically, rims are found to be the highest at the focal plane, z=0. There is an unavoidable large scatter in the data (approx. 20-30 nm), because of non-uniform thickness of the rim surrounding the crater..............................................................................58

Figure 3-15: Variation in the rim height to crater depth ratio with the distance of the sample surface from the focal plane. The ratio is highest at the focal plane, and decreases as the sample moves away from the focal plane in either direction...59

Figure 3-16: Summary of measured crater dimensions for different experimental set-ups. The highest values have been listed in this table to give an estimate of the orders of magnitude involved. ...................................................................60

Figure 3-17: Typical error bars for crater depth measurement as the lens moves closer to the glass sample. In this case, the focal length is 50 mm, pulse energy is 8 μJ, beam spot size is approximately 6.2 μm...........................................61

Figure 3-18: Typical error bars for crater rim height measurement as the lens moves closer to the glass sample. In this case, the focal length is 50 mm, pulse energy is 8 μJ, beam spot size is approximately 6.2 μm...........................................62

Figure 3-19: Typical error bars for rim height/crater depth ratio as the lens moves closer to the glass sample. In this case, the focal length is 50 mm, pulse energy is 8 μJ, beam spot size is approximately 6.2 μm...........................................62

x

Figure 3-20: Rim Height versus Crater Diameter. No particular trend seen. Data includes different focusing lenses, different pulse energies and different locations of the glass sample from the focal plane of the focusing lens. ........................63

Figure 3-21: Rim Height versus Crater Depth. No particular trend seen. Data includes different focusing lenses, different pulse energies and different locations of the glass sample from the focal plane of the focusing lens. .................................64

Figure 3-22: Rim Height/Crater Depth versus Crater Diameter. Data includes different focusing lenses, different pulse energies and different locations of the glass sample from the focal plane of the focusing lens. An inverse relationship is seen. .....................................................................................................65

Figure 3-23: Rim Height/Crater Depth versus log(Crater Diameter). Data includes different focusing lenses, different pulse energies and different locations of the glass sample from the focal plane of the focusing lens. A linear decreasing trend is seen. ..................................................................................................65

Figure 3-24: Effect of Numerical Aperture on Rim Height. Rim Height decreases with decreasing NA. Rim height is also seen to decrease with increasing fluence. All data points are at the rear focal plane of the focusing lens.Error! Bookmark not defined.

Figure 3-25: Variation of Rim Height/Crater Depth ratio with fluence. Rim Height/Crater Depth ratio decreases with decreasing NA. All data points are at the rear focal plane of the focusing lens. ........... Error! Bookmark not defined.

Figure 4-1: Schematic of Experimental Setup. The circular aperture is placed in the front focal plane of the achromatic focusing lens. The aperture and lens are fixed on the same translation stage and move towards the glass sample surface in controlled increments...............................................................................66

Figure 4-2: Variation in the single shot ablation crater width as the lens moves towards the glass surface. The x-axis is normalized by the Rayleigh range. The craters are widest at the focal plane, ‘z=0’. Beam profile = ‘top-hat’, NA = 0.28, aperture diameter = 3 mm, beam spot size ≈ 5 μm. This trend is different from that seen for ablation with a Gaussian beam profile. .....................................69

Figure 4-3: Variation in the single shot ablation crater depth as the lens moves towards the glass surface. The x-axis is normalized by the Rayleigh range. The craters are deepest at the focal plane, ‘z=0’. Beam profile = ‘top-hat’, NA = 0.28, aperture diameter = 3 mm, beam spot size ≈ 5 μm. The trend is the same as that for ablation with a Gaussian beam profile, although the reasoning is more involved. ................................................................................................70

Figure 4-4: Variation in fluence as the lens moves towards the glass sample. The x-axis is normalized by the Rayleigh range. The fluence is the maximum at the focal plane, as expected. Beam profile = ‘top-hat’, NA = 0.28, aperture diameter = 3 mm, beam spot size ≈ 5 μm. ...............................................................72

Figure 4-5: Variation in beam spot size as the focusing lens moves closer to the glass surface. The x-axis is normalized by the Rayleigh range. The spot size is the maximum at the focal plane and decreases as the sample moves away from the focal plane in either direction. At a relatively large distance from the focal plane, the spot size starts increasing again. Beam profile = ‘top-hat’, NA = 0.28, aperture diameter = 3 mm, beam spot size ≈ 5 μm. .....................................73

Figure 4-6: Variation in crater rim height as the focusing lens moves closer to the glass surface. The x-axis is normalized by the Rayleigh range. The rim height is maximum at the focal plane (Airy disk pattern) and decreases as the sample moves away from the focal plane in either direction (top-hat pattern). Beam

xi

profile = ‘top-hat’, NA = 0.28, aperture diameter = 3 mm, beam spot size ≈ 5 μm. .......................................................................................................74

Figure 4-7: Variation in rim height/crater depth ratio as the focusing lens moves closer to the glass surface. The x-axis is normalized by the Rayleigh range. The ratio seems to be steady till the Rayleigh range and then seems to decrease. This is in contrast to the trend seen with the Gaussian beam profile which is lowest at the focal plane (Figure 3-15). beam profile = ‘top-hat’, NA = 0.28, aperture diameter = 3 mm, beam spot size ≈ 5 μm. ..................................................75

Figure 4-8: Summary of experimental data for ‘top-hat’ Single Shot Ablation Craters............................................................................................................75

Figure 4-9: Variation in ratio of rim height by crater depth (b/h) with the square of crater diameter (D2). Diamonds indicate craters ablated with Gaussian beam profile, triangles indicate craters ablated with a largely truncated Gaussian beam, and the crosses are the craters with the glass surface some distance away from the focal plane, where the beam profile almost resembles a top-hat profile. The arrows indicate the datapoints which have been shown in Figure 4-10.............77

Figure 4-10: For craters with same depth = 220 nm and near threshold fluence, rim height is lower for top-hat crater than for the Gaussian crater. top-hat crater: f = 50 mm, E = 50 μJ, depth = 220 nm, width = 16 μm. Gaussian crater: f= 50 mm, E = 20 μJ, depth = 220 nm, width = 12.4 μm. The x-axis is in μm, y-axis is in nm. The data-points are indicated by arrows in Figure 4-9.............................78

Figure 4-11: AFM images of the top-hat and Gaussian craters compared in Figure 4-10. The top-hat craters are always circular and have a uniform rim as compared to the Gaussian craters..............................................................78

Figure 4-12: Variation in crater depth with distance from focal plane. The x-axis is normalized by the Rayleigh range. In case of both the Gaussian and the top-hat beam profiles, the crater depth decreases with increasing distance from the focal plane. In all cases shown, beam spot size ~ 6 micron. ..................................80

Figure 4-13: Rim height decreases for both Gaussian and top-hat beam profiles as we move away from the focal plane. The x-axis is normalized by the Rayleigh range. In all cases shown, beam spot size ~ 6 micron...................................80

Figure 4-14: rim height/crater depth Ratio decreases as the beam profile changes from airy disk to top-hat. The x-axis is normalized by the Rayleigh range. It behaves in the inverse fashion when the beam profile stays Gaussian all through. This shows that beam shaping is an effective method for controlling the crater rim height development. In all cases, spot size ~ 6 μm, depth ~ 700 μm.........81

xii

List of Tables

Table 1: Summary of General Trends as a function of Focal Plane Location............84

xiii

1 Introduction

1.1 Introduction and Motivation

Femtosecond lasers offer a revolutionary tool for micromachining micron-

scale three-dimensional structures either on the surface or in the bulk of any

material [1-7]. They offer accuracy of less than one-tenth of a micron in applications

requiring a high degree of precision such as tissue nanosurgery [8-12]. Being a

direct write process, a femtosecond laser micromachining set-up can be used to etch

complex geometries that can otherwise not be done by traditional lithographic

techniques. Again, the short time duration of the laser pulses can be exploited to

capture molecular level incidents by the laser [13-14].

All of this is possible because of the ultrashort duration of the pulses.

Extremely high peak intensities can be achieved while keeping the average power

low. The laser intensity is high enough to initiate non-linear absorption inside the

target substrate, thus causing ablation. On the other hand, the low average power

translates into minimal collateral damage. In other words, the damage is confined to

a tight volume inside the material.

Since the high peak intensity laser pulses can be absorbed inside the material

by a non-linear process, even transparent materials can be easily machined using a

femtosecond laser.

Although there are multiple advantages to using femtosecond laser

micromachining, the end result of multishot ablation is not very smooth. Cracks and

other microfeatures are seen in case of surface ablation of dielectric materials like

glass. These microfeatures can be explained by understanding the ablation process

with single laser pulses [15]. A single shot ablation crater is typically surrounded by

a 50-200 nm high rim. In case of multishot ablation, the rims of multiple craters

overlap and diffractively interfere, resulting in microfeatures, and thus surface

roughness.

53

The main purpose of this study is to experimentally study the rim formation

process in single shot ablation craters, and to identify factors that influence the rim

height, so that it can be reduced. Eliminating the crater rim should make the

femtosecond laser ablation process a perfect tool for applications requiring precise

and yet very smooth custom-designed channels, such as for lab-on-a-chip devices.

1.2 Theoretical Background

1.2.1 Femtosecond Ablation in Transparent Dielectrics

Glass is transparent because it is permeable to visible electromagnetic

radiation or in other words, no linear absorption takes place inside it. When an

ultrashort pulse laser (any wavelength) is incident on a dielectric like glass, the peak

intensity of the beam is so high that it manages to non-linearly impart enough

energy to the electrons to pull them from the valence to the conduction band, thus

making them free electrons. These electrons, in turn, act as seed electrons and free

yet more electrons by avalanche ionization. About 15-18 generations of avalanche

ionization yields a sufficiently large electron plasma density to exceed macroscopic

level ablation threshold.

At high laser energy, hot electrons and ions may explosively expand out of

the focal volume into the surrounding material. This explosive expansion (ablation)

leaves a void or a less dense central region surrounded by a denser halo.

Densification of glass by femtosecond laser pulses can also occur. Which of these

mechanism causes structural change depends on laser, focusing, and material

parameters.

Nonlinear photoionization (direct excitation of the electron from the valence to

the conduction band by the laser field) can happen in two ways depending on the

laser intensity and frequency. In tunneling ionization, the electric field of the laser

suppresses the Coulomb well that binds a valence electron to its parent atom. If the

electric field is very strong, the Coulomb well can be suppressed enough that the

15

bound electron tunnels through the short barrier and becomes free, as shown

schematically in the left-hand panel of Figure 1-1. This type of nonlinear ionization

dominates for strong laser fields and low laser frequency.

At high laser frequencies (but still below that required for single photon

absorption), an electron in the valence band absorbs enough photons so that the

number of photons absorbed times the photon energy is equal to or greater than the

band-gap of the material. This process, called Multiphoton Ionization, (MPI) is shown

in the right-hand panel of Figure 1-1. More details can be found in [16]. The

transition between tunneling ionization and MPI is decided by the Keldysh parameter

[17].

Figure 1-1: Schematic diagram of the photoionization of an electron in an atomic potential for different values of the Keldysh parameter. Tunneling Ionization is favored by strong laser field

and low laser frequency. Multiphoton Ionization (MPI) is the dominant method of photoionization for high laser frequencies. [16]

The avalanche ionization process is schematically shown in the Figure 1-2. It

involves free-carrier absorption followed by impact ionization [18]. An electron

already in the conduction band linearly absorbs several laser photons sequentially. In

order to conserve both energy and momentum, the electron must transfer

momentum by absorbing or emitting a phonon or scattering off an impurity when it

absorbs a laser photon. For electrons high in the conduction band, the deformation

potential scattering time is approximately 1 fs, so frequent collisions make free

carrier absorption efficient. After the sequential absorption of n photons, where n is

the smallest number that satisfies the relation nћω ≥ Eg, the electron’s energy

exceeds the conduction band minimum by more than the band-gap energy Eg. The

electron can then collisionally ionize another electron from the valence band, as

illustrated in the right-hand panel of Figure 1-2. The result of the collisional

16

ionization is two electrons near the conduction band minimum, each of which can

absorb energy through free carrier absorption and subsequently impact ionize

additional valence band electrons.

Figure 1-2: Avalanche Ionization. An initially free electron linearly absorbs several laser photons through free-carrier absorption, then impact ionizes another electron [16].

Interestingly, in the case of femtosecond laser pulses, photoionization by the

leading edge of the laser pulse provides the seed electrons for avalanche ionization

during the rest of the pulse [16]. Unlike the case with longer duration laser pulses,

this self-seeded avalanche process does not require free electrons to be already

present in the material in the form of surface/lattice defects or impurities, thus

making the ablation process much more repeatable, and consistent from sample to

sample. The femtosecond ablation rate, hence, depends on the material’s intrinsic

characteristics only (bandgap energy etc).

Energy is transferred from the free electrons to the heavy ions in the

picoseconds time scale. The ions further transfer the energy to the lattice in the form

of micrometer scale vibrations (exhibited as thermal effects on the macro-level) in

the nanoseconds time scale. Thus the ablation can be executed with minimal thermal

‘side-effects’; in other words, the ablation process is complete before the rest of the

lattice can realize it! Ultimately, precise and controllable processing with minimal

collateral thermal damage can be achieved compared to other laser machining

approaches.

In comparison, in case of machining with nanosecond laser pulses, there is

weak linear absorption in glass in the visible and the near infrared (NIR) range. The

17

pulse energy is thus absorbed in an extended volume in the glass, leading to thermal

expansion inside, and hence increased internal stresses. This causes macro-cracking

in the inherently brittle glass sample, limiting the precision of the machining process.

1.2.2 Accounting for Undesirable Effects

Non-linear effects and optical aberrations can cause the laser beam to get

spatially and temporally distorted, thus affecting the ablated crater morphology and

also introducing error into the measurement of factors such as the laser pulse energy

and beam spot size at the sample surface. These factors need to be accounted for

during the experiment. A brief discussion about the same is given below.

1.2.2.1 Non-Linear Propagation Effects – Self-focusing

Self-focusing is a result of the intensity dependence of the refractive index

[19]

Innn 20 += …(1.1)

where n is the total refractive index, n0 is the ordinary linear refractive index

coefficient and n2 is the nonlinear refractive index coefficient. The spatial intensity

profile in the laser pulse (usually Gaussian) leads to a spatial refractive index profile:

because n2 is positive in most materials, the refractive index becomes higher at the

center of the beam compared to the wings. This variation in refractive index acts as

a lens and focuses the beam.

As the power in the laser pulse is increased, self-focusing becomes stronger

until, at some critical power, it balances diffraction and a filament is formed. If the

peak power of the laser pulse exceeds this critical power for self-focusing then

catastrophic collapse of the laser beam to a singularity is predicted [19]. The critical

power, Pcr, is given by

20

22

8)61.0(nn

Pcrλπ

= ...(1.2)

18

where λ is the laser wavelength. For borosilicate glass, n0 = 1.52 and n2 = 3.4 x10-16

cm2/W [20] and thus Pcr = 1.8 MW.

In reality, as the laser beam self-focuses, the intensity rises and eventually

becomes sufficient to nonlinearly ionize electrons in the free space. The electron gas

contributes a negative refractive index change that cancels the positive refractive

index change produced by the intensity-dependent index and prevents further self-

focusing [21][22].

The laser intensity at the laser focus in the presence of weak self-focusing, Isf,

increases with increasing peak power, P, according to [16]

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=

cr

sf

PPII

1 ...(1.3)

where I is the laser intensity in the material in the absence of self-focusing.

While the threshold for optical breakdown and damage depends on the laser

intensity, the threshold for self-focusing depends on peak power. If the laser pulse is

tightly focused into the material using an external lens, the intensity for optical

breakdown can be reached with powers that are below the critical power for self-

focusing.

In transparent solids, the critical power is typically of the order of 1 MW (as

calculated above) and the intensity threshold for bulk optical breakdown using a

femtosecond laser pulse is about 1013 W/cm2.

In the present analysis the energies used in the set-up are much higher than

the critical energies, and hence the equations should account for self-focusing.

19

1.2.2.2 Optical Aberrations

Spherical aberrations occur when light rays at different heights from the

optical axis are focused by the lens at slightly different distances along the axis.

Since the maximum Numerical Aperture (NA) used in the experiments is 0.08,

therefore spherical aberrations do not pose an issue for us [16].

Chromatic aberrations are caused when different wavelengths of the light

incident on the focusing lens are not focused at exactly the same focal plane. The

femtosecond laser used in the experiment has a wavelength bandwidth of about 9

nm only, hence this type of aberrations are not of concern in the experiment.

A coma aberration occurs due to rays entering the focusing lens at an angle,

resulting in a circular object being imaged as a ‘coma’ in the imaging plane of the

lens. This is minimized by ensuring that laser beam is normally incident on the lens

(by looking at the back-reflection), and by using high quality optics.

1.2.3 Undesirable Damage during Femtosecond Ablation

Process

Most of the incident laser energy goes into creating an electron plasma in the

thin upper layer on the material. As the electron density in the plasma increases, it

becomes more reflecting and more absorbing [23]. Due to the large electron density

in that layer, it starts behaving like a metal; drastically decreasing the transmission,

and hence limiting the ablation depth. The laser created surface plasma acts as a

filter transmitting only the leading edge of the laser pulse. The transmitted energy is

approximately fixed, nearly independent of the input pulse energy.

The rapid energy deposition in a thin surface layer creates an extremely large

energy density, leading to intense shocks and a high pressure gradient in the zone.

An immediate rapid rarefaction wave compensates for the shock. Both these effects

contribute to increased stress in the material leading to microcracks. Most of the

53

energy ends up getting reflected from the surface, along with the high energy

plasma.

Perry et al. [24] have shown that for high fluences (F>5-10 Fth, where

threshold fluence, Fth ~ 2 J/cm2 for fused silica), a large portion of the energy is

reflected from the sample surface. For a laser fluence of ~ 1014 W/cm2, they show

that a few microseconds after irradiation, about 70% of the absorbed energy is used

by the expanding plasma to move the ambient gas. 20% of the absorbed energy is

lost as radiation to the environment, ultimately leaving less than about 3% of the

incident laser energy as heat inside the material.

This thermal energy causes a thin layer of molten glass to be formed

immediately beneath the ablation crater. The lifetime of the molten layer (including

both the melting and resolidification processes) depends on how quickly the energy

gets dissipated into the bulk. This depends on the material thermal properties

(thermal conductivity, specific heat, density etc) [15].

Ben-Yakar et al [25] show that the melt flow in the borosilicate glass sample

is caused principally by hydrodynamic forces due to the pressure gradient caused by

the hot plasma sitting over the melt. The pressure gradient is extremely high at the

edges of the ablated crater at the plasma/air interface. This results in some of the

molten glass being ejected out of the crater over the edges of the crater. Rapid

solidification results in the formation of a high rim surrounding the crater.

When craters are formed by multiple laser shots on the glass surface, the

rims of the individual craters are seen to interact and influence each other [15]. This

happens because the second laser pulse diffracts through the edges of the previously

formed crater and creates a modulated light intensity at the bottom of the crater due

to the interference of the diffracted light in the near field. This results in a ripple

formed next to the crater rim. Similarly the third pulse gets diffracted again at the

edges of the existing crater, leading to more microfeatures. The cumulative effect

shows up as a macro-level surface roughness in the ablated structure.

21

Depending on the number of overlapping laser pulses at one spot on the

substrate, the roughness can be exhibited as microfeatures, or as macrofeatures, or

it can even be eliminated by self-annealing during the micromachining process

[26][27].

Also, melting followed by a rapid cooling to the ambient temperature causes

residual tensile stresses on the glass surface [28]. Ashkenasi et al. [29] have found

that the hardness on the laser ablation crater edge is larger by at least a factor of six

relative to non-illuminated areas when ablated with a 700 fs laser pulse. Therefore

when an additional laser pulse is introduced near the area modified by the previous

pulse, cracks will appear because of increased internal stresses.

1.2.3.1 In-Depth Discussion about the Crater Rim

As discussed above, the main force in play during the ablation process is due

to the pressure gradient applied by the expanding plasma onto the molten material

lying underneath. This plasma pressure forces the molten glass towards the

periphery of the crater, thus directly influencing the free surface at the interface

between the plasma and the melt. The molten layer at the edge of the crater faces

an extremely high pressure gradient at the interface between the plasma and air.

This pressure difference pushes the melt over the crater surface very rapidly. The

pressure driven flow time τp thus determines the elevation of the melt above the

surface, or in other words, this time duration decides the height of the rim. A shorter

τp results in a higher elevated resolidified rim.

The characteristic time scale for this pressure-driven melt flow is [25]:

20

2

mp hp

Lμτ ≈ …(1.4)

where hm is the average melt depth, p0 is the average plasma pressure, μ is the

viscosity and L is the crater width.

The melt depth is a function of the optical and thermal properties of the

substrate, prominent factor being the threshold fluence for ablation for that material.

22

Based on heat transfer calculations, Ben-Yakar et al. [25] have estimated the melt

depth to be of the order of about 1 μm and its lifetime τm to be of the order of about

1 μs.

With the estimated melt temperature exceeding 2500 K, the glass viscosity μ

can be taken to be as small as 1 Pa.s [see Appendix B]. Typical crater width can be

assumed to be 10 μm. The plasma pressure drops from a few millions of

atmospheres at the start of ionization to about 10 atm after about 100 ns. Thus the

average plasma pressure over the 100 ns time duration can be assumed to be ≈

1000 atm. Hence, using equation 1.4, we estimate the pressure driven flow time, τp,

to be of the order of about 100 ns.

Hence the pressure-driven flow time and the melt flow time are almost of the

same order of magnitude. In case of τp being smaller than τm, the melt gets pushed

out faster before it can resolidify, thus resulting in a rim.

Extending the above logic, since τm is almost constant for a given

experimental set-up, therefore the rim height should have an inverse relationship

with the time τp. Thus,

2

20

Lhpb m

μ≈ …(1.5)

where b is the rim height.

hm is almost constant for a given material. An increase in the fluence implies

an increase in the plasma pressure and temperature. This results in a melt with

higher temperature, and hence lower viscosity. Both these factors contribute to

decreasing the pressure-driven flow time, which in turn results in a higher rim.

Hence rim height is directly proportional to the fluence. Since crater depth is a

function of fluence, this translates into the direct proportionality between the rim

height and the crater depth. Also, from equation 1.5, the rim height decreases as the

crater width increases.

23

Therefore we expect to see a relationship between the rim height, crater

width and the crater depth, such that the rim height is a function of crater

depth/(crater width)2, ie., b ∝ h/L2.

1.2.4 Possible Methods for Improving Machining Quality

In this project we try to design an experiment to improve the smoothness of

channels made by multishot femtosecond laser ablation. Below we discuss some of

the possible theoretical ways of doing this.

Use of minimum threshold fluence

Surface roughness seen in multishot ablation channels are because of the

rims of individual craters formed by single pulses. Use of near threshold fluences

during single spot ablation results in almost rimless craters. However the crater

width and depth are extremely small and hence this method is not of much

commercial use for obtaining smooth multishot ablation craters. Additionally the

crater dimensions become more variable from shot-to-shot when we work in this

fluence range.

Top-Hat beam profile

This method can also be used to reduce rim heights of single shot ablation

craters, and has been explored in greater detail in the next chapter.

Pre- and post-machining annealing of glass

Stresses are developed in borosilicate glass when different parts of the crater

made by a single femtosecond laser pulse cool down at different rates and can

ultimately result in micro- or macro-cracking. These internal stresses can be relieved

in the glass substrate by slowly heating it to the annealing point – the temperature

at which the molecular arrangement is so altered within a reasonable period of time

that the internal stresses disappear. After the internal stresses have been removed,

the temperature is lowered very slowly so that all regions of the mass are at

24

practically uniform temperature during the cooling. This is to make sure that the

mass shrinks uniformly and no strains develop.

It has been shown that annealing of glass sample, either before or after the

ablation experiment, results in reduction of the height of bumps formed in glass by a

laser [30]. The bump width remains unaffected. The reduction depends on the

annealing conditions to a large extent. Also, the results are more drastic when the

annealing is done after the ablation experiment.

Also, heating the glass substrate during the ablation experiment can ensure

minimal cracking and hence better surface quality.

Machining conditions (inert gas stream, vacuum)

It is a well established fact that the use of an inert gas blowing at a steady

velocity and pressure over the sample surface during the ablation experiment helps

to blow away the debris created during the ablation resulting in cleaner ablation. Sun

et al. [31] show that nonlinear self-focusing and plasma defocusing in an air or

nitrogen environment can significantly distort the focused laser beam profile.

However this distortion can be minimized by use of an inert gas shield, particularly

helium, thus resulting in improved machining quality and efficiency.

Similar improvements in ablation craters have been made while performing

the experiment inside a vacuum chamber.

1.3 Thesis Objectives

The ultimate objective of this project is to identify the factors that influence

rim formation in craters created by single shot ablation of dielectric materials. The

sample of choice is borosilicate glass.

Different techniques are tried to reduce the crater rim height, with special

focus on reshaping the spatial intensity distribution of the beam from a Gaussian to a

top-hat.

25

2 Laser Beam Spatial Profile

2.1 Gaussian Beam Theory

The subject of Gaussian beam propagation has been well researched [32].

However, a clear understanding of the terminology and the characteristics of the

Gaussian beams is crucial in order to fully appreciate the experimental design and

results. Hence, at the risk of repetition, some relevant discussion and definitions are

given below for the reader’s quick reference.

The Fourier transform of a Gaussian is a scaled Gaussian both in the near

field and in the far field (unless intentionally reshaped); thus the beam profile

remains Gaussian at every point along its path of propagation through the optical

system. This makes it very convenient to work with lasers. Hence, most lasers are

designed such that they resonate with a Gaussian distribution of the electric field.

The electric field distribution E(r,z) along the transverse (r) and axial (z)

direction, measured in Volts/m is given by [32]:

( ) ( ) ( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛+−−⎟⎟

⎠

⎞⎜⎜⎝

⎛ −= zi

zRrikikz

zwr

zww

EzrE ζ2

expexp,2

2

20

0 …(2.1)

Here, E0 is the peak electric field amplitude at the focal plane at the axis, w0 = beam

waist, w(z) = beam radius at an axial location z, r is the radial co-ordinate, R(z) =

radius of curvature at z. k = 2π/λ = wave number, for the design laser wavelength λ.

The time-averaged intensity distribution [W/m2] is given by:

))(

2exp())(

(2

),(),( 2

220

0

2

zwr

zww

IzrE

zrI −==

η …(2.2)

As before, I0 is the peak electric field intensity at the focal plane at the axis. η is the

characteristic impedance of the medium in which the beam is propagating. For free

space, η = η0 ≈ 377 Ω.

26

It is easier to measure the field intensity rather than the amplitude; hence the beam

waist is normally calculated in terms of the field intensity. For the sake of

consistency, the beam waist w0 is defined in this thesis as the radial distance from

the axis where the intensity falls to 1/e2 (or 0.135) of the peak intensity at the axis.

w(z) is defined as the beam waist, where the electric field amplitude E0 and intensity

I0 drop to 1/e and 1/e2, respectively, at any axial location, z.

At the focal plane (z = 0), the transverse variation of electric field is hence given by:

)exp()( 20

2

0 wrErE −

= …(2.3)

And the electric field intensity is

)2exp()( 20

2

0 wrIrI −

= …(2.4)

Hence, both E(r) and I(r) are Gaussian in shape.

As the Gaussian beam propagates, it experiences diffractive spreading beyond

a certain distance, and hence the beam does not stay collimated over long distances.

Thus, the beam radius and the radius of curvature change with axial distance.

The radius of curvature of the beam changes as

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=

2201)(zw

zzRλ

π …(2.5)

and the radius of the beam changes as

27

( )2/12

20

0 1⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=

wzwzw

πλ

…(2.6)

where λ is the wavelength of light, z is the distance propagated from the plane where

the wavefront is flat, w0 is the beam waist, R(z) is the wavefront radius of curvature.

These trends are shown in the Figure 2-1 and Figure 2-2 below:

Figure 2-1: Change in beam profile and wavefront radius of curvature of Gaussian Profile with propagation distance [by courtesy of Melles Griot Inc.]

Figure 2-2: Growth in beam diameter as a function of distance from the Gaussian beam waist [by courtesy of Melles Griot Inc.]

The common parameter in eqns 2.5 and 2.6 is the Rayleigh range and is

defined as the axial range over which the beam can be considered to be collimated.

It is also called the confocal parameter. It is the axial distance from the focal plane

where the beam cross-section becomes twice that at the focal plane, and can be

considered to be the dividing line between the near-field and the mid-field range.

Mathematically,

28

λπ 2

0wzR = ...(2.7)

R(z) is infinite at z = 0 (flat wavefront implies infinite radius of curvature, and hence

z = 0 defines the beam waist location), passes through a minimum at z = zR, and

rises again toward infinity as z is further increased, asymptotically approaching the

value of z itself.

At distances much beyond the Rayleigh range, the beam starts to diverge as a

spherical wave from a point source located at the center of the waist. The half-angle

divergence of the Gaussian TEM00 beam can be calculated as (Figure 2-1 and Figure

2-2):

0

)(wz

zwπ

λθ == ...(2.8)

Also, beyond zR, the beam radius increases linearly along the axial direction, as

0

)(wzzw

πλ

≅ ...(2.9)

The radius of curvature starts increasing linearly beyond the Rayleigh range:

( ) zzzzzR R ≅

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+=

2

1 ; z ⟩⟩ zR ...(2.10)

All these equations are true on both sides of the focal plane.

2.1.1 M2 Beam Propagation Factor

The fundamental TEM00 Gaussian mode of the laser beam ensures the

smallest cross-section and the smallest divergence in the near field of the beam.

Hence for applications requiring the laser beam to be focused to a small spot, the

TEM00 mode is the ideal mode for the spatial beam profile. However, in the real

world, this is almost impossible to achieve for a femtosecond laser beam. The higher

the laser power, and the more complex the excitation mechanism for lasing to

happen, the higher the deviation from a pure Gaussian profile. Truncation of the

beam by any limiting apertures in the laser cavity also introduces fringes around the

29

main beam, thus affecting the beam profile. Presence of unnecessary harmonic

modes in the beam profile causes the laser parameters to be unpredictable and

unstable with time, and hence need to be accounted for in calculations.

Since a multimode combination of beams can have a nearly perfect Gaussian

shape, calculations based on the Gaussian fit can be misleading. Instead, the M2 (M-

squared) beam propagation factor defined by Siegman [33] outlines a way of

characterizing a laser, such that the exact focused spot size can be predicted for a

given input beam width and lens focal length. Taking this one step further, the

irradiance at a focused spot, the Rayleigh range and the far-field divergence of the

beam can be calculated using the M2 factor.

For a pure Gaussian beam [34],

θ = w0/zR = w0/(π w02/λ) = λ/π w0 = 2λ/πd0

where d0 and θ are the beam waist width and half divergence angle for an ideal

Gaussian beam, zR is the Rayleigh range, w0 is the beam waist radius, and λ is the

wavelength.

This gives:

πλθ 2

0 =d ...(2.11)

Real beams have a diameter-divergence product higher than the fundamental limit

by a factor of M2.

Thus, for real laser beams,

⎟⎠⎞

⎜⎝⎛=Θ

πλ42

0 MD ...(2.12)

where D0 and Θ are the actual beam waist width and half divergence angle.

30

An interesting (though not typical) case is that of an ‘embedded Gaussian beam’

(shown in Figure 2-3). In this case, the real beam is everywhere larger than the ideal

beam by M, thus forcing the divergence to be larger by a factor of M, thus

( )( )θMMdD 00 =Θ (embedded Gaussian beam)

Since divergence is calculated as θ = 2w0/zR, therefore

zR = 2w0/θ = d0/θ = D0/Θ for an embedded Gaussian beam, i.e., Rayleigh range is

the same for an embedded Gaussian beam.

Figure 2-3: Embedded Gaussian beam. This case occurs quite infrequently. [by courtesy of Melles Griot]

Note that for usual cases, the M2 factor can affect the beam waist size and/or the

divergence, in any ratio.

Hence equations 2.5 and 2.6 get modified giving the radius and wavefront curvature

of a real Gaussian beam with the following equations:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=

2

2

201)(zM

wzzR R

R λπ

31

( )2/12

20

2

0 1⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=

RRR w

zMwzwπ

λ ...(2.13)

where w0R is the beam waist size of the real beam, wR (z) and RR (z) are the beam

radius and wavefront curvature of the real laser beam at distance z from the beam

waist, respectively.

2.1.1.1 Measuring M2 factor

M2 value is measured for the laser pulses of the femtosecond amplifier using the

procedure outlined in the Appendix A.

The beam propagation factor is measured to be different along the x- and y- axes:

Mx2 = 1.8 ± 0.04

My2 = 1.2 ± 0.07

The difference between Mx2 and My

2 is because the beam is slightly elliptical and it

focuses at slightly different distances from the focusing lens along the two transverse

axes.

2.2 Reshaping the Gaussian Beam Profile into Top-Hat

2.2.1 Introduction

The main intent of the project is to find methods of reducing surface

roughness observed in micromachining with femtosecond lasers. As discussed

earlier, this roughness seems to be the result of the rims seen to surround single-

shot ablation craters. Reshaping the laser beam can offer a possible solution for this

problem, as discussed below.

32

The most popular laser beam profile is the Gaussian intensity distribution,

because it has the minimum divergence and stays collimated over a relatively long

working range of a few hundred meters, depending on the beam diameter. This

profile is excellent for alignment purposes. However, in case of machining with the

Gaussian beam profile, the energy carried in the wings of the Gaussian distribution

does not contribute effectively to the ablation process and is therefore wasted. This

results in a lower part throughput and hence a higher production cost per part. Also,

Gaussian beams can result in poor edge quality because the spatial energy

distribution contributes to a wider heat-affected-zone (HAZ) around the illuminated

area. Poor edge quality with signs of melting and spatter is observed. This is

undesirable in applications involving drilling, scribing, marking or annealing.

In the case of micromachining with femtosecond laser pulses, the increased

HAZ because of the Gaussian beam profile would cause relatively more substrate

material to be molten, hence increasing the rim heights of the craters and the splash

around the crater formed by single shot ablation. Overall this would show up as

increased surface roughness.

Theoretically, if the Gaussian beam is spatially reshaped such as the intensity

gradient in the outside region of the focused laser beam profile is increased, making

the edges of the profile much steeper, with a uniform intensity profile in the middle

portion, this top-hat or flat top profile should give an ablation crater profile with

characteristics similar to the beam profile: straighter side-walls, uniform bottom.

(Figure 2-4) It is expected that the ablation rate of the material will exhibit a spatial

profile which is a mirror image of the incident beam intensity profile, removing at

higher rates at the edges than at the center, as compared to ablation with a

Gaussian beam.

The sharper edges of the beam profile should result in a smaller heat-affected

zone along the sides of the crater, and hence less associated collateral damage, melt

and crater rim formation. As compared to the original Gaussian function, the top-hat

behaves like an energy step function with either enough energy to cause ablation or

none at all. A melt zone will still be created beneath the ablation depth of the crater.

33

But there will be a lesser melt on the sides of the crater, ultimately leading to a

smaller elevated rim around the crater.

(b) (a)

Figure 2-4: Comparison between (a) Gaussian and (b) top-hat laser beam profiles [Courtesy of Newport Corporation]

Also, if one uses multiple top-hat laser pulses, the walls of the crater so

generated should be much smoother and more vertical as compared to the walls of

the crater made by multiple Gaussian pulses.

Experiments done by Karnakis et al. [35] using a top-hat beam profile for

machining polymers and silicon nitride (ceramic) with a Nd:YAG nanosecond pulse

laser demonstrate improved edge quality, reduced roughness and wall roughness

and a significant reduction in the energy density required for drilling microholes of

high aspect ratio.

2.2.2 Theory behind Reshaping Gaussian into Top-Hat

A focusing lens behaves like a Fourier transform device; it performs a two-

dimensional Fourier transform of the incident waveform at the speed of light. If an

object (eg. transparency or aperture) is placed in the front focal plane of the lens

and illuminated with coherent collimated light, the optical field at the back focal

34

plane of the lens will be the Fourier transform of the input object. This is a very well

researched and well-understood phenomenon [36].

The project requires to create a uniform intensity profile at the focus of a

lens. An inexpensive way of making a top-hat is by truncating the Gaussian beam

with a small circular aperture. A Gaussian beam incident on a small diameter circular

aperture behaves similar to a plane wave incident on a ‘hard edge’ circular aperture.

When the ‘plane wave’ truncated by the aperture (‘circ’ function) is focused by a

focusing lens, a Fourier transform of the aperture, an Airy disk pattern, is formed in

the rear focal plane of the lens. This is in contrast to the focused image of the

untruncated Gaussian beam, which is a scaled Gaussian, as discussed above.

If the distance between the aperture and the focusing lens is different from

the focal length f, then a phase factor is introduced in the Fourier transform at the

focal plane. This phase factor cannot be detected by the human eye or a beam

profiler since both read the intensity pattern, and hence any information carried in

the phase is thus lost. This phase factor can however be observed using

interferometric methods. If the laser fluence is close to the threshold fluence for

ablation, this additional phase factor might affect the ablation characteristics to some

extent. In order to minimize this factor, the aperture is placed in the front focal plane

of the lens. A typical experimental set-up is shown in Figure 2-5.

f

SampleFocusing Lens Focal PlaneAperture z

Direction of Translation

f

Figure 2-5: Schematic of Experimental Setup. A circular aperture is placed in the front focal plane of the achromatic focusing lens. Both the aperture and lens are translated together

towards the glass sample surface.

35

The far field diffraction pattern of a source is observed in the focal plane of a

focusing lens. This is because the wavefront is almost flat at the focal plane, which is

the defining characteristic of the far-field regime (section 2.1). In contrast, outside

the Rayleigh range of the focal plane, the curvature of the wavefront starts

increasing linearly with distance from the focal plane, as per equation 2.10. The

diffraction pattern transitions from far-field at the focal plane to mid-field beyond the

Rayleigh range, and then finally near-field much further away from the focal plane.

In the far-field, the diffraction pattern is the exact Fourier transform of the

object, albeit scaled in size. In the near field region, the diffraction pattern varies in

both shape and size as we move away from the focal plane. Hence, when the object

is a circularly truncated plane wave (top-hat) as in this experiment, the image

resembles an Airy disk (Fourier transform of a top-hat) at the focal point of the lens.

In the mid-field regime, the image is a combination of a top-hat and an Airy disk.

The image becomes a perfect top-hat in the near-field region. This transition can be

seen in Figure 2-6.

Figure 2-6: Schematic of typical beam profiles in the near field (laser output), far field (at the focus of a lens), and intermediate field [37]. The sharp edge aperture forms the top-hat wave-front which becomes the object for the focusing lens. Fraunhofer diffraction pattern is seen at

the focal plane and Fresnel diffraction pattern is seen away from the focal plane.

36

In the real case, the sharp edges of the aperture introduce Fresnel rings into

the beam profile (Figure 2-7). However, since the energy variation is about 10% and

the walls are very sharp and straight (instead of the usual Gaussian profile) this

should serve as a good top-hat for our purpose. Also, the diffraction ripples get

smoothened out with distance, and hence better results are expected as the target

moves away from the focal plane in either direction. Ideally, a soft edge aperture

such as one with a Gaussian transmission function with 100% transmission at the

center and decreasing transmission towards the edges should result in a Fourier

transform without diffraction fringes.

Figure 2-7 therefore proves that using a truncating aperture provides a low

cost solution for reshaping the laser beam, requiring minimal implementation effort.

A major disadvantage of using this method is that the aperture cuts off a lot

of energy and hence this is a wasteful method, if implemented for commercial

purposes for generating flat top beams. However it works successfully in providing a

proof of concept for the current project.

37

Z=0 μm

Z=1500 μm Z=-1500 μm

Z=5000 μm Z=-5000 μm

Figure 2-7: Beam profiler images of typical beam profiles in the near field (z= ±5000 μm), far field (z= ±0 μm), intermediate field (z= ±1500 μm). The images are made with a 10X NA 0.28 objective lens, with an aperture with diameter 3 mm in its front focal plane. The incident beam is expanded from 8 mm to 22 mm before the aperture. The beam profile represents an Airy disk

at z = 0, and approaches a top-hat as we move away from the focal plane.

2.2.3 Alternative Methods for Creating a Top-Hat

The ideal method for generating a top-hat beam profile is to create a

propagating Airy disk before the lens, such that the Fourier transform of the Airy

profile (represented mathematically by a Bessel function) is a top-hat at the focal

plane [38]. This can be done using a Diffractive Optics Element (DOE). For the

desired focusing lens, we need to back-calculate the Fraunhofer transform pattern of

the desired top-hat and then design a DOE element specific to that particular airy

disk. Thus the set-up requires a customized DOE to be designed for every focusing

lens. Also, the efficiency and effectiveness of a DOE also depends on the M2 and the

stability of the laser, which can be quite variable, depending on the optics. All factors

put together, making a DOE can be an expensive proposition.

38

An alternative method of producing a top-hat is by using a pair of lenses to

image a circular aperture. However, a real image is formed beyond the focal plane of

the second lens. This is undesirable when working with a high power femtosecond

laser since the focused beam causes non-linear ionization in the air, leading to the

ionization of air at the focal plane, which can unpredictably change the beam profile.

The best method of creating a reliable top-hat beam profile is by modifying

the laser cavity itself. For a given beam diameter, the lower the order of the mode,

the lower the divergence. Consequently, for applications that involve focusing the

beam to a small spot, or for propagating the beam over long distances, the laser

should be constrained as best as possible to the TEM00 mode. However, if the main

requirement is maximum power per unit volume, or if a constant intensity across the

beam (a "top-hat" profile) is required, then a stable cavity that operates in a high-

order mode will be appropriate.

39

3 Ablation with Gaussian Beam Profile

Surface ablation of borosilicate glass is carried out using high energy single

femtosecond laser pulses with Gaussian energy distribution. The results are

compared with those in existing literature, in order to gain experience in the

experiments, and to calibrate our experimental set-up and procedure against known

techniques. Once the ablation and imaging technique is well established and

standardized, the effect of different ablation parameters (such as numerical aperture

and pulse energy) on the rim height of the crater is studied.

3.1 Design of Experiment

The experimental set-up is quite simple and is shown in Figure 3-1. A

combination of a half-wave plate and a cubic beam splitter are used for controlling

the pulse energy (and hence, fluence). A focusing lens of focal length f is fixed on a

z-axis 25 mm travel translation stage with a 0.5 μm step-size and placed in the path

of the raw untruncated beam from the amplifier exit. The lens focuses the beam on a

clean borosilicate glass sample (thickness 1.1 mm), which is fixed on an x-y-

translation stage at approximately the rear focal plane of the lens. By checking the

back reflection of the laser beam from the front surface of the sample, the sample is

made normal to the direction of the incident laser beam.

Single shot ablation experiments are carried out with different laser pulse

energies ranging from approximately 10 μJ to 1000 μJ. Also, the variation in crater

morphology is studied while moving the target away from the focal plane of the lens.

40

f

Target

Focusing Lens

Cubic Beam Splitter

Half-Wave Plate

Beam Dump


Figure 3-1: Top-View of Experimental Setup. The focusing lens is on a translation stage and is moved towards the glass sample in controlled step-sizes during the ablation experiment.

3.1.1 Setup Details

3.1.1.1 Laser system

The experiments are done with a kilohertz repetition rate Ti:Sapphire

amplifier (Spitfire, Spectra Physics, Mountain View, CA) with the following

specifications:

Pulse Energy (@ 1 KHz): ~ 1 mJ

Centerline wavelength: 780 nm

Pulse length at exit: ~130 fs

Beam diameter: 7.5 ± 0.5 mm (at 1/e2 of peak intensity), Gaussian spatial profile

Beam Propagation Factor, M2: M2x = 1.8, M2

y = 1.2

Polarization: linear, horizontal

Energy amplification is achieved in the amplifier using ‘Chirped Pulse

Amplification’ (CPA); the technique involves temporally stretching the pulse,

λ=780 nm, τ ≈ 130 fs Regenerative Amplifier

Energy < 1 mJ @ 1 KHz repetition frequency

Femtosecond Oscillator

Pump

Pump

41

amplifying it at reduced peak power, and then recompressing the amplified pulse

near the exit, to close to its original pulse duration.

A single femtosecond duration pulse is isolated from the mode-locked pulse

train from the femtosecond oscillator (Tsunami, Spectra Physics, Mountain View,

CA), and becomes the ‘seed pulse’ for the amplifier. If this pulse is directly amplified,

it can develop enough energy to destroy the gain medium through non-linear

processes like self-focusing inside the crystal. To avoid this catastrophe, the CPA

technique is used, whereby a diffraction grating first temporally stretches out the

seed pulse by slowing down the high frequency components of the femtosecond

pulse. This method works especially well for ultrashort pulses, since the bandwidth is

large for a small laser pulse width (for a Gaussian pulse, ΔνΔt > 0.441, where Δν is

the bandwidth, and Δt is the pulse width). The positively chirped pulse is now

introduced into the gain medium of the amplifier while the crystal is being

simultaneously optically pumped by the 1 kHz repetition rate frequency doubled 532

nm Nd:YLF laser. Pockels cells with response times of a few nanoseconds serve to

ensure multiple passes of the seed pulse through the amplifier Ti:Sapphire, thus

amplifying the pulse by about 10 times with each pass. An optimum number of

passes of the pulse through the crystal ensures maximum cavity gain, maximum

pulse energy and minimum pulse-to-pulse energy fluctuation. This requires that the

instant when the amplified seed pulse is ejected from the gain cavity by the Pockels

cell be carefully monitored. Finally the amplified pulse is recompressed to the original

pulse width through the exact reverse process using another diffraction grating

(negative chirp).

3.1.1.2 Energy Measurement

Pulse energy is measured after the focusing lens (immediately before the

target) using a high-resolution energy meter by reducing the repetition rate of the

amplifier from 1 kHz to 10 Hz and averaging over 1000 points. Pulse-to-pulse

fluctuation is measured to be about 0.5%. During the actual ablation experiment, the

continuous lasing mode of the amplifier is disabled, and the Pockels cell allows only

one pulse at a time to be amplified inside the cavity. This causes the temperature of

42

the Ti:Sapphire crystal to drop. Therefore, for accurate pulse energy measurement,

the repetition rate is decreased to 10 Hz to create the same environment inside the

cavity (low operating temperature) as during the actual experiment.

3.1.1.3 Borosilicate Glass Substrate

Majority of this study was carried out on borosilicate glass (1.1 mm thick

samples from ‘Precision Glass and Optics Ltd.’), also known as BorofloatTM.

Borosilicate glass is chemically inert, hydrophilic, optically 100% clear, and relatively

inexpensive and is therefore a favorite with chemists and biologists. This justifies our

choice of substrate for this experiment. The properties of borosilicate glass are listed

in Appendix B. The glass sample is cleaned with ‘optical grade’ methanol in an

ultrasonic bath before and after each ablation experiment, to get rid of any debris or

dust.

3.2 Post Ablation Analysis

Following laser processing, the sample with the single shot ablation craters is first

observed under a reflection optical microscope (20X, 50X, 100X magnification) to

measure the crater diameters in order to estimate the focal plane. It is also used to

look at the quality of the prepared sample, before SEM and AFM analyses.

The crater morphology (depth, rim, presence of debris etc) is studied in detail by

scanning the sample under an Atomic Force Microscope (AFM) (Digital Instruments

Dimension 3100 with Nanoscope IV controller) under ambient conditions. All AFM

topographic images are collected in the tapping mode by use of a 10 nm tip radius

Silicon cantilever (MikroMasch) with a typical resonant frequency of 315 kHz and

typical force constant 14.0 N/m.

Some of the craters are also observed under a Scanning Electron Microscope (SEM)

(model: Hitachi S-4500 Field Emission SEM) operating at about 20 kV accelerating

43

voltage. Secondary electron images are generated to obtain 2-D information on the

crater size, shape, recast layer, and crack formation at various locations.

3.3 Experimental Procedure

Keeping the laser energy fixed, the focusing lens is translated towards the

sample surface in small controlled step sizes (Figure 3-2), and five single shot

ablation craters are made on the sample surface for each axial position, to ensure

statistical consistency. The single shot craters are at least 200 microns apart from

each other, to make sure there are no diffraction effects because of the craters being

too close [15].

The focal plane is estimated by using a knife-edge technique (razor blade and

a beam profiling CCD camera). The knife is later replaced by the clean borosilicate

glass sample. Estimating this location with a card using the naked eye is difficult

because ablation can start much before the focal plane in case of a long confocal

range. Also, the CCD camera can be used for looking at the focal plane, but since the

exact location of the CCD array chip in the camera is difficult to measure accurately,

this method is not good for locating the focal plane. After the single shot ablation

experiment, the crater widths can be measured and the trend of the ellipticity can be

used to accurately pinpoint the focal plane (Figure 3-2). This is discussed in more

detail in section 3.5.1.

All experiments are performed in air at atmospheric pressure.

44

Sample (fixed)

Focusing Lens


Focal Plane

f

z

a)

b)

μ

100 μm beyond Focal Plane At Focal Plane 100 μm before Focal Plane Scale

Figure 3-2: a) The focusing lens translates towards the target in all the experimental runs. Single shot ablation is carried out starting from the sample placed beyond the focal plane, till

when it lies much before the focal plane. b) Sample optical images of single-shot ablation craters: E = 20 μJ, beam spot size = 6.2 μm, Gaussian beam profile, fluence ~ 16 J/cm2

3.3.1 Data Available

Single shot ablation craters were made on the surface of borosilicate glass with the

following experimental parameters:

f = 50 mm, NA = 0.08, E = 8,10,20,30,40,60,80 μJ

f = 100 mm, NA = 0.04, E = 32, 40, 80, 120 μJ

f = 250 mm, NA = 0.02, E = 103, 500, 1065 μJ

where f = focal length; NA = Numerical Aperture; E = pulse energy

45

3.4 Qualitative Analysis

The Numerical Aperture (NA) of an optical set-up characterizes the range of

angles over which the system accepts or emits light. In the present context, if a laser

beam of diameter 2w0 is incident on a lens of focal length f, the NA equals:

fw

fw

NA 00

22

== …(3.1)

Theoretical focused spot size,NAw

fwπ

λπ

λ==

01

Rayleigh range, λ

π 21wzR =

Therefore, the higher the NA, the tighter the focusing and hence smaller the

focused beam spot size. The Rayleigh range becomes short too.

Since the NA used in all experiments is less than 0.65, there is no concern for

spherical aberration [16].

For high pulse energies, self-focusing needs to be accounted for in the

experiments. As discussed in section 1.2.2.1, critical peak power for self-focusing to

start is 1.8 MW. For a 200 fs pulse duration laser, the minimum average pulse

energy required is 1.8x106 x 200x10-15 = 3.6x10-7 W = 0.36 μJ. This condition is

fulfilled in all cases considered in this thesis. Hence the resulting laser intensity at

the focus needs to be adjusted accordingly.

The self-focusing effect is especially prominent when the target lies beyond

the focal plane, because the non-linear focusing of the laser beam in the air causes

air-ionization and plasma breakdown, thus causing distortions in the beam profile.

The non-elliptical crater shape and their non-uniform rims validate this reasoning.

This can however be corrected by performing the experiments in a vacuum chamber

at a pressure below 10-4 mbar [39].

53

Again, since all experimentation is done with single laser pulses, self-focusing

should not be a problem for the cases with the glass surface either at or before the

focal plane, unless very high fluences are used (> 20 J/cm2).

1. Glass sample beyond the focal plane:

Careful perusal of Figure 3-3 shows the presence of an inner deeper elliptical

region embedded inside the single shot ablation crater. Air dissociation starts to

occur at an intensity of 4 x 1013 W/cm2. Hence if the fluence is high enough, the air

can get ionized at the focal plane, creating charged plasma that enhances the

ablation of the glass surface in an uncontrolled manner. The distortion of the beam

profile at the focal plane also results in non-elliptical craters.

Craters formed by tighter focusing exhibit uniform rims surrounding the craters

and decreased debris. On the other hand, as the NA of the set-up decreases

(implying looser focusing and larger crater sizes), the debris increases and the rim

becomes relatively non-uniformly distributed around the periphery of the crater. This

non-uniformity seems to follow a trend. Higher rims are seen on the sides of the

ellipse across the major axis of the inner ellipse. This could be because along the

high curvature boundary, the molten material finds lesser area to get redeposited in,

leading to the higher rim.

47

Figure 3-3: Optical image for single shot ablation crater made with f = 250 mm, E = 1000 μJ, with the glass sample beyond the focal plane of the lens. The non-uniform rim seems to be

caused by the material ejected from the inner elliptical crater, and higher layer of material is deposited where there is lesser circumference available for deposition.

2. Glass sample at the focal plane:

There is a sharp, relatively high and uniformly distributed rim outside the crater.

A typical example is shown in Figure 3-4.

Figure 3-4: Optical images for single shot ablation craters made with f = 250 mm, E = 1000 μJ, with the glass sample at the focal plane of the lens. The rim is relatively high, and uniformly

distributed around the crater boundary.

3. Glass sample before the focal plane:

All craters are elliptical in shape and are usually almost rimless (Figure 3-5).

There seem to be two levels of ablation – the inner crater is deeper, and the so-

called rim of the inner crater (formed of debris) is typically lower than the sample

surface. There is a shallow ‘moat’ surrounding this inner crater and this might or

might not have a rim slightly higher than the background surface. Since the focal

plane is well inside the glass sample, or even behind it, there is just enough fluence

available at the glass surface to cause minimal ablation. Most of the laser pulse is

just enough to cause thermal melting of the glass. On cooling, this might cause the

48

material to compress and sink lower than the surface level. Or, as discussed by

Schaffer et al [16], this could happen because of densification of glass by

femtosecond pulses by breaking bonds in the material through multiphoton

ionization.

Figure 3-5: Optical images for single shot ablation craters made with f = 250 mm, E = 1000 μJ, with the glass sample before the focal plane of the lens. The inner rim is formed of debris and

is uniform. These craters are typically rimless.

3.5 Quantitative Analysis

3.5.1 Crater Width, Beam Spot Size, Focal Plane Location

The single shot ablation craters made using the Gaussian beam profile are

elliptical in cross-section, owing to the ellipticity of the laser beam. Optical images of

the single shot ablation craters are used to measure the crater diameter along the

horizontal direction, and also along the major and minor axes of the elliptical craters.

Sample data is shown in the Figure 3-6 below:

49

0

5

10

15

20

25

30

35

40

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Distance from Focal Plane [normalized]

Cra

ter

Wid

th [

μm

]

horizontal axismajor axisminor axis

Figure 3-6: Variation in crater width as the lens moves closer to the glass surface. The x-axis is normalized by the Rayleigh range. There is a dip in the trend at the focal plane, as expected. Gaussian beam profile, f = 100 mm, E = 120 μJ. Crater width is measured along a) the axis of

AFM scanning, b) major axis of elliptical crater, c) minor axis of elliptical crater. For later analysis, crater widths are measured along the major axis of the ellipse, to maintain

consistency.

The trend is seen to be the same for the measurements along the major and

minor axes respectively. For most of the analysis ahead, consistency is maintained

by using the width measured along the major axis of the elliptical crater.

Increasing numbers on the x-axis of all the plots depicts the focusing lens

moving closer to the glass sample. In other words, ‘relative axial location’ less than

‘zero’ implies that the glass sample is beyond the focal plane. ‘z = 0’ implies that the

sample surface is exactly at the focal plane. Positive values indicate that the sample

surface is closer to the lens than the focal distance. Refer to Figure 3-2 for

experimental sketch.

At the focal plane, the crater width is expected to be the smallest. As we

move away from the focal plane in either direction, the crater width should start

increasing, gradually within the Rayleigh range and then steeply outside it. This is

because the beam spot size in diverging while there is sufficient fluence to cause

ablation.

50

The change in ellipticity (ratio of major diameter to minor diameter) of the

elliptical craters as the lens moves towards the glass surface is graphed in Figure 3-7

below. Contrary to the expected trend, ellipticity is not the minimum at the focal

plane. Since the beam propagation factor M2 is different for the laser beam in the x-

and y- directions, the beam focuses at slightly different distances from the lens in

the two transverse directions, which causes the focal spot to be slightly elliptical too.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Distance from Focal Plane [normalized]

Ellip

tici

ty

(maj

or d

ia/m

inor

dia

)

Figure 3-7: Typical case of variation in ellipticity of the elliptical single shot ablations craters as the lens moves closer to the glass sample. The x-axis is normalized by the Rayleigh range. No

particular trend is observed.

Figure 3-8 below compares the variation in the crater width for different

energies for a sample experimental set-up.

51

0

5

10

15

20

25

30

35

40

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Cra

ter

Wid

th [

μm

]

32 microJ40 microJ80 microJ120 microJ

Figure 3-8: Variation of Crater Width as the Glass Sample moves towards the focusing lens, f = 100 mm (Experimental Data). beam spot size at focus = 13.9 μm. The x-axis is normalized by

the Rayleigh range.

Given the average laser pulse energy Eavg and fluence Favg, and the average

threshold energy and fluence Ethavg and Fth

avg, the crater diameter can be estimated

as [39]:

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛= =

thNth

avgo

EEw

FF

wD ln2ln2 201

20

2 ...(3.2)

where w0 is the beam spot size (radius) and D is the crater width at that location.

Focal length, f = 100 mm

Incoming beam radius, w0 = 4 mm

Wavelength, λ = 780 nm

Ideal beam spot size (radius) at the focal plane, w1’ = fλ/πw0 = 6.2 μm

Estimated beam propagation factor M2 = 2

Expected beam spot size (radius) at the focal plane, w1’’ = 12.4 μm

Using an estimated beam spot size of 12.4 mm, we get the following crater width

distribution with ‘z’ (Figure 3-9):

52

Figure 3-9: Expected variation in crater width with decreasing axial distance between the lens and the glass sample. This trend is seen to match with the experimental trend of Figure 3-6.

Hence, the experimentally obtained trends match with the simulations.

The focal plane is roughly estimated during the experiment by using a knife-

edge and a beam profiler CCD. This value can be accurately estimated but since the

knife-edge is replaced by the actual glass sample during the experiment, the focal

plane location tends to shift by a few hundred microns. During the data analysis, the

widths of the single shot ablation craters are measured using an optical microscope

and plotted against z, the distance of the sample from the focal plane, as shown in

Figure 3-8 above. The craters are expected to be the smallest at the focal plane,

based on the MATLAB simulations. Based on this knowledge, the focal plane is then

estimated. All the graphs in this thesis have been accordingly recalibrated.

The slope of the plot of the measured crater sizes D at different fluences (at a

particular axial location) yields the beam spot size at that particular ‘z’, based on

equation 3.2. Sample data is shown in Figure 3-10 for an arbitrary z location of

‘z=1700’.

53

D2 = 500log10(E) - 1405.7

0

200

400

600

800

1000

1200

1 10 100 1000(log) Energy (E) [μJ]

(Cra

ter

Dia

met

er)2 (

D2 )

[ μm

]2

Figure 3-10: Variation in (crater diameter)2 with energy for a given axial location of the glass surface with respect to the focusing lens (z/zR = -0.2). The beam spot size at each ‘z’ can be

calculating by finding the slope of each curve and using equation 3-2.

Air dissociation starts to occur at an electron intensity of 4 x 1013 W/cm2.

Assuming the femtosecond pulse duration to be about 200 fs by the time the laser

pulse reaches the target, air ionization starts as soon as the fluence is more than 4 x

1013 W x 200 x 10-15 = 8 J/cm2. Hence, fluences significantly higher than 8 J/cm2

cause the data points to deviate from a linear trend [39].

The beam spot size so obtained for different ‘z’ values is then plotted against

‘z’ to show how the beam spot size varies as the focusing lens moves closer to the

glass sample. This value is a function of the incoming beam size w0, lens focal length

f, laser wavelength λ, and is independent of the laser pulse energy. Figure 3-11

shows the case for f = 100 mm, incoming beam waist (radius) = 4 mm.

54

0

5

10

15

20

25

-400 -300 -200 -100 0 100 200 300 400

Distance From Focal Plane [μm]

Bea

m S

pot

Size

Rad

ius

[μ

m]

Figure 3-11: Variation in beam spot size with axial distance ‘z’ (distance between the glass surface and focusing lens). Calculated using analysis based on Figure 3-10. f = 100mm. Beam

spot size at focal plane is approximately 13.9 μm.

From Figure 3-11, the actual beam spot size measured at the focal plane is w1 =

13.9 μm. The ideal beam spot size (calculated above for f = 100 mm, w0 = 4 mm) is

6.2 μm. Therefore calculated “Beam Propagation Factor” (M2) is 13.9/6.2 = 2.2. This

is close to the directly measured value of M2 of 1.8 (section 2.1.1.1) and is

acceptable within experimental error. Also, the Rayleigh range, zR is 778 μm.

The Rayleigh range value is used to normalize the axial location of the glass

sample surface w.r.t the focal plane of the focusing lens. This ensures that data

obtained for experiments with different focused beam spot sizes and widely different

energies can be compared with each other.

Equation 3.2 and Figure 3-10 are also used for estimating the single shot

ablation threshold energy and hence fluence using the y-intercept value of the graph.

FthN=1 is calculated for this experiment to be ranging between 2 to 2.5 J/cm2.

55

3.5.2 Crater Depth

The crater ablation depth for a single-shot ablation crater can be estimated

using the following equation, as long as the fluence is much higher than the

threshold fluence.

⎟⎟⎠

⎞⎜⎜⎝

⎛= >

−1

01 ln Nth

avg

effa FF

h α …(3.3)

αeff-1 is the effective optical penetration depth, and is assumed to be 240 nm

when ablating in air [39]. FthN>1 is the multishot threshold fluence for the substrate

calculated to be equal to 1.7 J/cm2 (independent of atmospheric conditions).

Equation 3-3 is used for estimating the variation in the crater depth as the

distance between the lens and the target varies, for the case of the lens with focal

length f = 100 mm, and for different energies. The theoretical data is plotted using

MATLAB in Figure 3-12 shown below. The crater is expected to be the deepest at the

focal plane, where the fluence is the highest.

Figure 3-12: Calculated Crater Depth Variation with Distance from Focal Plane. The craters are deepest at the focal plane.

56

Experimental data for the crater depth obtained from the AFM scanned

images is plotted in Figure 3-13 below:

0

50

100

150

200

250

300

350

400

450

500

-1.50 -1.00 -0.50 0.00 0.50 1.00 1.50


Cra

ter

Dep

th [

nm

]

80 microJ120 microJ

Figure 3-13: Experimental data for variation in crater depth as the lens moves closer to the glass surface. Beam profile: Gaussian, beam spot radius = 13.9 μm, f = 100 mm. The x-axis is

normalized by the Rayleigh range.

The trend for the crater depth is as almost as expected from the MATLAB

simulations. The actual measured crater depth values are however consistently about

150-200 nm smaller than the expected values. Most probably this can be explained

by a discrepancy in the value of the optical penetration depth, which has been

assumed to be 240 nm, based on literature survey [39].

It is interesting to note that the craters are the deepest when the distance of

the glass sample surface is slightly less than the focal distance from the lens. When

the focal point is within the glass sample, it should logically cause more material to

be ablated, hence creating a deeper crater. However, since the sample has a finite

thickness of 1100 μm, once the focal point moves outside the sample, much lesser

material is ejected from the crater, causing the depth of the craters to decrease.

The crater depths for the 80 μJ craters are almost the same as expected.

However, the depths for the higher 120 μJ craters are much lower. This could be

57

because once a critical free electron density has been created on the crater surface,

any additional fluence is unable to create any more plasma, and cause additional

damage. All the extra energy is simply reflected from the surface.

3.5.3 Crater Rim Height

The rim heights are measured from the AFM scanned images of the craters.

Data for single shot ablation craters made with f = 100 mm, and 80 and 120 μJ pulse

energies is plotted in the Figure 3-14 below.

0

10

20

30

40

50

60

70

80

90

-1.50 -1.00 -0.50 0.00 0.50 1.00 1.50


Rim

Hei

ght

[nm

]

80 microJ120 microJ

Figure 3-14: Variation in rim heights as the glass sample moves closer to the focal plane. The x-axis is normalized by the Rayleigh range. Typically, rims are found to be the highest at the

focal plane, z=0. There is an unavoidable large scatter in the data (approx. 20-30 nm), because of non-uniform thickness of the rim surrounding the crater.

This trend cannot be easily modeled using a simple equation, since the rim

formation is a result of complex physical phenomena. However it is plainly visible

from the experimental data that the rim heights are the highest when the sample

surface is at the focal plane, and then the rim heights keep reducing as the sample

moves either towards or away from the focusing lens. Since the fluence is highest at

the focal plane, accordingly, the ablation depth is the largest and the crater size is

58

the smallest here. The melt zone is therefore larger in this case. It has to spread

around a smaller crater perimeter in a relatively short period of time, leading to a

higher rim.

In this particular case, the rims vary between 80 nm to rimless craters. The

fluctuation is of the order of about 30 nm.

Rim heights below 20 nm in my experiments are considered to be almost

rimless. The rim heights are quite scattered because sometimes it is difficult to

clearly differentiate between the rim and the splash due to the scattered debris. The

main issue of concern in this thesis is the rim around the crater formed due to

resolidification of the molten layer. Logically, this rim seems to be the main culprit

behind the lack of smoothness in multishot ablation channels. The debris created

during the ablation process gets loosely stuck to the glass surface and can be easily

gotten rid of by etching with mild NaOH for a few minutes.

To better understand the trend, we normalize the rim height by the crater

depth for each crater. The variation in the normalized rim height as the lens moves

closer to the target surface is shown in Figure 3-15 below:

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

-1.50 -1.00 -0.50 0.00 0.50 1.00 1.50

Relative Axial Location [normalized]

Rim

Hei

ght/

Cra

ter

Dia

met

er 80 microJ

120 microJ

Figure 3-15: Variation in the rim height to crater depth ratio with the distance of the sample surface from the focal plane. The ratio is highest at the focal plane, and decreases as the

sample moves away from the focal plane in either direction.

59

As in case of Figure 3-10, the rim height/crater depth is the highest at the

focal plane and then it decreases as the sample moves away from the focal plane in

either direction.

Similar ablation experiments with single laser pulses are performed on

borosilicate glass, using plano-convex lenses of different focal lengths (f = 50 mm,

100 mm, 250 mm) (and hence different Numerical Apertures), with different pulse

energies and at varying distances from the focal plane. The incoming beam diameter

is the same as that from the amplifier exit. All these different experimental settings

serve to change the crater morphology (diameter, depth, rim height) by changing

the fluence and focusing conditions.

The data so obtained is compiled into separate graphs and is available in the

Appendix C. The trends seen with all the different focusing lenses are similar to the

ones discussed above for f = 100 mm. A summary of all the compiled data is given

in Figure 3-16. This helps to give an idea of the orders of magnitude involved.

NA f [mm] w1 [μm]

(maxm)

h [nm]

(maxm)

b [nm]

(maxm)

b/h

(maxm)

0.08 50 24 700 180 0.45

0.04 100 33 400 80 0.22

0.02 250 100 450 20 0.15

Figure 3-16: Summary of measured crater dimensions for different experimental set-ups. The highest values have been listed in this table to give an estimate of the orders of magnitude

involved.

NOTE: NA = Numerical Aperture, f = focal length, w1 = focused beam spot size, h = crater

depth, b = rim height, b/h = rim height/crater depth ratio.

3.5.4 Error Analysis

The crater width is measured using images from the optical microscope and from the AFM scans. The accuracy of the readings is ± 0.2 μm. The limitation in the measurement is because of the spread out crater rims which make it difficult to pinpoint the exact edge of some of the single-shot ablation craters. The relative error is therefore typically of the order of ± 1%.

60

Typical error bars for measurement of crater depth are shown in Figure 3-17. The average accuracy for the depth measurement is about 20 nm. The uneven bottoms and the presence of some debris in some craters results in this fluctuation in measurement. The relative error therefore varies from about 4 to 8% for different crater depths.

0

50

100

150

200

250

300

350

-100 -50 0 50 100

Rel Axial Value [μm]

Cra

ter

Dep

th [

nm

]

Figure 3-17: Typical error bars for crater depth measurement as the lens moves closer to the glass sample. In this case, the focal length is 50 mm, pulse energy is 8 μJ, beam spot size is

approximately 6.2 μm.

Figure 3-18 shows typical error bars in the measurement of rim heights of single shot craters. The fluctuation is about ± 20 nm. However this value changes a lot depending on the experimental conditions, and varies between 10 nm to 60 nm. The presence of debris, and the non-uniformity of the rims leads to this high error. For a typical 10 to 100 nm rim height, this implies a relative error ranging from 20 to 200%. In most cases, the measurements and analysis are done based on a physical understanding of the process. Data points with very high relative error have not been used for the overall analysis.

61

0

20

40

60

80

100

120

140

-100 -50 0 50 100


Rim

Hei

ght

[nm

]

Figure 3-18: Typical error bars for crater rim height measurement as the lens moves closer to

the glass sample. In this case, the focal length is 50 mm, pulse energy is 8 μJ, beam spot size is approximately 6.2 μm.

The error measurements for the crater depth and rim height shown in the

plots above are mathematically combined to find the error for the rim height/crater depth ratio, and some typical data is plotted in Figure 3-19. We see a very high fluctuation in the data. Only data-points with errors that can be physically justified have been used for the overall analysis.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

-100 -50 0 50 100


Rim

Hei

ght/

Cra

ter

Dep

th

Figure 3-19: Typical error bars for rim height/crater depth ratio as the lens moves closer to the

glass sample. In this case, the focal length is 50 mm, pulse energy is 8 μJ, beam spot size is approximately 6.2 μm.

62

3.6 Overall Conclusions from the Entire Dataset

As per the discussion about the crater rims in section 1.2.3.1, we expect to

see a relationship between the rim height and the crater width and depth.

Accordingly, we plot the variation in the rim height with the crater diameter and with

crater depth in Figure 3-20 and Figure 3-21 below. This dataset includes data for

different ways of changing the crater dimensions including

• different pulse energies

• different beam spot sizes using different focusing conditions, and

• different beam spot sizes using different distances from the focal plane

There is no clear trend of how the rim height changes with the crater diameter and

depth.

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60 7

Crater diameter, D [μm]

Rim

Hei

ght,

b [

nm

0

]

Figure 3-20: Rim Height versus Crater Diameter. No particular trend seen. Data includes different focusing lenses, different pulse energies and different locations of the glass sample

from the focal plane of the focusing lens.

63

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000

Crater Depth, h [nm]

Rim

Hei

ght,

b [

nm]

Figure 3-21: Rim Height versus Crater Depth. No particular trend seen. Data includes different focusing lenses, different pulse energies and different locations of the glass sample from the

focal plane of the focusing lens.

Next, for each crater, the ratio of the rim height to crater depth is plotted

against the crater depth (Figure 3-22). A distinct inverse relationship is seen

between the three parameters. The plot shows that the crater width, depth and rim

height are interconnected.

A detailed comparison between Figure 3-22 and Figure 3-23 shows that the

possible relationship between b/h and D is:

b/h ∝ 1/D2

or

Rim height/Crater Depth (b/h) is inversely proportional to the square of

Crater Width (D2)

64

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30 40 50 60 7

Crater Diameter [μm]

Rim

Hei

gh

t/C

rate

r D

epth

0

Figure 3-22: Rim Height/Crater Depth versus Crater Diameter. Data includes different focusing lenses, different pulse energies and different locations of the glass sample from the focal plane

of the focusing lens. An inverse relationship is seen.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Crater Diameter2 [μm2]

Rim

Hei

gh

t/C

rate

r D

epth

Figure 3-23: Rim height/crater depth versus (crater diameter)2. Data includes different

focusing lenses, different pulse energies and different locations of the glass sample from the focal plane of the focusing lens. An inverse ‘1/x’ relationship is seen.

65

4 Ablation with Top-Hat Beam Profile

Surface ablation of borosilicate glass is carried out using high energy single

femtosecond pulses, which have been reshaped by truncating the incoming Gaussian

beam with a circular aperture. The results are compared with the results from the

previous chapter (ablation with the Gaussian beam profile), in order to understand

the effect of reshaping the beam into a top-hat spatial profile. Explanation has been

offered for the observations, though it needs to be validated using appropriate

modeling.

4.1 Experimental Setup & Procedure

The experimental set-up is the same as in Figure 3-1 except that a circular aperture is placed in the front focal plane of the lens, (ie. a distance f before the lens). Both the aperture and the

lens are on a translation stage arranged to move in the axial direction in small increments. The borosilicate glass sample is fixed on an x-y-translation stage and is positioned normal to the

direction of the incident laser beam. The schematic is shown in

Figure 4-1.

f

SampleFocusing Lens Focal PlaneAperture z


f

Figure 4-1: Schematic of Experimental Setup. The circular aperture is placed in the front focal plane of the achromatic focusing lens. The aperture and lens are fixed on the same translation

stage and move towards the glass sample surface in controlled increments.

66

The experiment is set up in such a way that we should get an Airy disk at the

focal plane, which has characteristics of the far-field regime. As we move outside the

Rayleigh range of the focused beam spot in either direction, the beam profile should

become a mixture of an Airy disk and a top-hat (see section 2.2.2). In the near-field

region, the profile should look more like a top-hat (Figure 2-6). This set-up can be

modeled based on Fresnel diffraction in the near-field region and Fraunhoffer

diffraction in the far-field (at the focal plane).

This has been verified by mapping the spatial intensity profile of the beam

using a beam profiler, as can be seen in Figure 2-7. Note that since a hard edge

aperture is used to truncate the beam, this leads to diffraction fringes in the beam

profile that can be clearly seen in the images.

Single shot ablation experiments are carried out with different laser pulse

energies ranging between approximately 5 μJ to 500 μJ, and with two different NA

lenses. Also, the variation in crater morphology is studied while moving the target

away from the focal plane of the lens.

An achromatic doublet is used as the focusing lens in this set of experiments in

order to ensure that all the wavelengths get focused at the same axial distance from

the lens. This is necessary in order to achieve the best possible top-hat beam profile.

Keeping the laser energy fixed, the aperture and focusing lens are translated

towards the sample surface in controlled small step sizes (Figure 4-1), and five

single shot ablation craters are made on the sample surface per axial position, to

ensure statistical consistency. The single shot craters are at least 200 microns apart

from each other, to make sure there are no diffraction effects because of the craters

being too close [15].

All experiments are performed in air at atmospheric pressure.

67

4.1.1 Data Available

Single shot ablation craters were made on the surface of borosilicate glass with the

following experimental parameters:

f = 20 mm, NA = 0.28, E = 7.7, 12.5, 15.2, 20.5, 24 μJ

f = 50 mm, NA = 0.035, E = 50, 80, 296, 409 μJ

where f = focal length; NA = Numerical Aperture; E = pulse energy

4.2 Discussion about the observed trends

Trying to simulate the behavior of the beam profile at and around the focal

plane is a very involved process, since we expect to see an Airy disk at the focal

plane, but a combination of a top-hat and an Airy disk beyond the Rayleigh range of

the focused beam spot. The area of interest is this combination of the two different

intensity distribution profiles.

4.2.1 Crater Width

At the focal plane, the beam profile is an Airy disk, rather than a Gaussian

distribution. For an aperture diameter 2w0 = 3.5 mm and a focusing lens with focal

length f = 20 mm (NA = 0.28),

Radius of Airy disk = w1 = 1.22 λf/2w0 = 5.4 μm.

Yura et al [40] show that for the same aperture to beam diameter truncation ratio,

the radius of the beam spot size at the focal plane is

w1 = 1.28fλ/D

= 1.28 * 20 * 0.780 / 3.5 = 5.7 μm

This spot size calculated this way is about 5% larger than that calculated using the

Airy Disk assumption and thus the two theories corroborate.

68

On the other hand, beam waist expected for a Gaussian profile is

w1 = fλ/πw0 = 2.8 μm

By measuring crater sizes created by multiple pulse energy settings, and

using the method used in section 3.5.1 for estimating the beam spot size, we find

that the profile at the focal plane is indeed an Airy disk.

Sample data for variation of crater diameter with axial displacement is shown

in Figure 4-2 below. As the focal plane moves inside the sample, the beam profile

starts approaching a top-hat. For an incident laser beam with a fixed given pulse

energy, the radius of a top-hat is 1/√2 times the radius of a Gaussian. Accordingly,

away from the focal plane, the beam spot size and hence the crater size will be much

smaller than that predicted for a usual Gaussian beam, leading to a smaller crater

size. This is exactly what we see in the experiment.

0

1

2

3

4

5

6

7

8

9

10

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5


Cra

ter

Wid

th [

μm

]

7.7 microJ12.5 microJ15.2 microJ20.5 microJ24 microJ

Figure 4-2: Variation in the single shot ablation crater width as the lens moves towards the glass surface. The x-axis is normalized by the Rayleigh range. The craters are widest at the

focal plane, ‘z=0’. Beam profile = ‘top-hat’, NA = 0.28, aperture diameter = 3 mm, beam spot size ≈ 5 μm. This trend is different from that seen for ablation with a Gaussian beam profile.

Note that we do not need to account for the M2 propagation factor while

working with this set-up, since the aperture acts like a spatial filter and cleans out

69

the beam to a certain extent, thus reducing the M2 factor and hence reducing the

divergence from a perfect Gaussian TEM00 beam.

All craters are very circular when the truncated beam is used for ablation. In

the case of the Gaussian beam, the ellipticity of the craters was used to estimate the

focal plane. This can not be done when the aperture is in place, and the focal plane

needs to be estimated by looking for other symmetry in the measurements. In Figure

4-2, the focal plane seems to lie where the craters become the widest.

4.2.2 Crater Depth

The crater depth is seen to be the highest at the focal plane and the craters

become shallower as the target moves away from the focal plane (Figure 4-3).

0

100

200

300

400

500

600

700

800

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Cra

ter

Dep

th [

nm

]


Figure 4-3: Variation in the single shot ablation crater depth as the lens moves towards the glass surface. The x-axis is normalized by the Rayleigh range. The craters are deepest at the focal plane, ‘z=0’. Beam profile = ‘top-hat’, NA = 0.28, aperture diameter = 3 mm, beam spot size ≈ 5 μm. The trend is the same as that for ablation with a Gaussian beam profile, although

the reasoning is more involved.

The trends for the crater width and depth can be understood correctly only if

the change in fluence and the beam spot size can be mapped as the distance

70

between the lens and the sample surface decreases. This can be done by employing

the now-familiar equations:

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛= =

thNth

avgo

EEw

FF

wD ln2ln2 201

20

2 …(4.1)

⎟⎟⎠

⎞⎜⎜⎝

⎛= >

−1

01 ln Nth

avg

effa FF

h α ...(4.2)

where ha is the ablation depth, αeff-1 is the effective optical penetration depth, and

equals 240 nm when ablating in air [15]. F0 denotes average fluence; FthN>1 is the

multishot threshold fluence for borosilicate glass calculated to be equal to 1.7 J/cm2

(independent of atmospheric conditions). D is the crater width and w0 is the beam

spot size (radius) at that axial location. FthN=1 is the single-shot threshold fluence for

the substrate calculated to be equal to 2 J/cm2.

Variation in average fluence as a function of the distance of the lens from the

target can be estimated by using equation 4.2 with the measured values of ha as a

function of ‘z’. Figure 4-4 below shows that the fluence is highest at the focal plane

and decreases as the lens moves further from or closer to the sample.

71

0

5

10

15

20

25

30

35

40

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Flu

ence

[J/

cm2 ]


Figure 4-4: Variation in fluence as the lens moves towards the glass sample. The x-axis is normalized by the Rayleigh range. The fluence is the maximum at the focal plane, as expected.

Beam profile = ‘top-hat’, NA = 0.28, aperture diameter = 3 mm, beam spot size ≈ 5 μm.

Similarly, equation 4.1 can be used with the measured values of crater

diameter D and the above-calculated values of fluence F0avg to model how the beam

spot size w0 changes as the distance between the lens and the sample changes.

Although the equation is originally derived for the case of ablation by a Gaussian

beam, it is safe to assume that the trend of the variation in diameter for craters

made by a top-hat beam would be similar. We find that the spot size stays almost

constant till the Rayleigh range (Figure 4-5). With higher energies and thus more

data points, the beam spot size is seen to increase beyond the Rayleigh range,

because of beam diffraction.

72

0

1

2

3

4

5

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Bea

m S

pot

Size

[μ

m]


Figure 4-5: Variation in beam spot size as the focusing lens moves closer to the glass surface. The x-axis is normalized by the Rayleigh range. The spot size is the maximum at the focal plane

and decreases as the sample moves away from the focal plane in either direction. At a relatively large distance from the focal plane, the spot size starts increasing again. Beam

profile = ‘top-hat’, NA = 0.28, aperture diameter = 3 mm, beam spot size ≈ 5 μm.

Unlike the Gaussian beam profile, the spot size does not increase

monotonically as we move away from the focal plane, because the increase in spot

size because of diffraction is compensated by the decrease due to the transition of

the beam profile from an Airy disk into a top-hat.

Theoretical modeling of fluence distribution is more involved and we depend

on the estimated trend for the fluence for varying axial location of the sample as

done in Figure 4-4. The peak fluence at the focal plane causes the crater width and

depth to be the highest at the focal plane. The decreasing fluence as the focal plane

moves farther from the glass surface justifies the monotonically decreasing crater

dimensions away from the focal plane.

73

4.2.3 Crater Rim Height

The trend in rim heights measured for the case of single shot ablation craters

made with a top-hat beam of beam spot size radius 5 μm is shown in Figure 4-6.

0

20

40

60

80

100

120

140

160

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Rim

Hei

ght

[nm

]


Figure 4-6: Variation in crater rim height as the focusing lens moves closer to the glass surface. The x-axis is normalized by the Rayleigh range. The rim height is maximum at the focal plane

(Airy disk pattern) and decreases as the sample moves away from the focal plane in either direction (top-hat pattern). Beam profile = ‘top-hat’, NA = 0.28, aperture diameter = 3 mm,

beam spot size ≈ 5 μm.

The rim heights are typically the highest when the focal plane is at the glass surface.

This is similar to what was observed in case of the Gaussian craters (Figure 3-14).

In Figure 4-7, we plot the ratio of the rim height to the crater depth against

the axial displacement for each crater, to check for any significant trends. It seems

to be steady within the Rayleigh range and decreases beyond it indicating that the

rim height and crater depth decrease at the same rate initially and then the rim

height starts decreasing more sharply.

74

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Rim

Hei

ght/

Cra

ter

Dep

th


Figure 4-7: Variation in rim height/crater depth ratio as the focusing lens moves closer to the glass surface. The x-axis is normalized by the Rayleigh range. The ratio seems to be steady till the Rayleigh range and then seems to decrease. This is in contrast to the trend seen with the Gaussian beam profile which is lowest at the focal plane (Figure 3-15). beam profile = ‘top-

hat’, NA = 0.28, aperture diameter = 3 mm, beam spot size ≈ 5 μm.

Graphical trends for more data points are shown in the Appendix E. The

trends for the rim height seem to be mostly consistent from experiment to

experiment although a large scatter is seen the data. This is because of the difficulty

of delineating the cause of the rim (melt or debris), especially in case of wider

craters.

NA f [mm] w1 [μm]

(maxm)

D [μm]

(maxm)

h [nm]

(maxm)

b [nm]

(maxm)

b/h

(maxm)

0.035 50 18 37 500 40 0.13

0.035 50 18 27 300 40 0.15

0.28 20 5 9 700 130 0.23

Figure 4-8: Summary of experimental data for ‘top-hat’ Single Shot Ablation Craters

NOTE: NA = Numerical Aperture, f = focal length, w1 = focused beam spot size, D = crater

diameter, h = crater depth, b = rim height.

75

4.3 Comparison between ‘Gaussian’ and ‘Top-Hat’ Craters

As shown in section 3.5.4, the rim height is a function of the crater width and

crater depth. Figure 4-9 below plots the variation in rim height/crater depth with the

crater diameter. The crater diameter is changed in the dataset by the following

methods:

• different pulse energies

• different distances from the focal plane, and

• different beam spot sizes using different focusing conditions.

The diamonds in the graph represent the craters ablated with the Gaussian beam

profile, as also shown in Figure 4-9. The triangles represent all the craters ablated

with the sharply truncated Gaussian beam. Among these data points, those which

are beyond the Rayleigh range (where the beam profile resembles a top-hat) are

represented with the crosses.

As a trend, the rim height/crater depth ratio for the top-hat craters is lower

than that for the Gaussian craters. Among the top-hat craters themselves, the ratio

seems to decrease with increasing crater width, as is the case for the Gaussian

craters.

It is easy to see that the rim height/crater depth ratio for single shot ablation

craters is more a function of the crater width than of the beam profile.

76

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 500 1000 1500

Crater Diameter2 [μm2]

Rim

Hei

ght/

Cra

ter

Dep

thGaussianTruncated GaussianTophat (sorted out)

Gaussian for fig.4-14

tophat for fig.4-14

Figure 4-9: Variation in ratio of rim height by crater depth (b/h) with the square of crater diameter (D2). Diamonds indicate craters ablated with Gaussian beam profile, triangles indicate

craters ablated with a largely truncated Gaussian beam, and the crosses are the craters with the glass surface some distance away from the focal plane, where the beam profile almost resembles a top-hat profile. The arrows indicate the datapoints which have been shown in

Figure 4-10.

77

-250

-200

-150

-100

-50

0

50

100

150

-20 -15 -10 -5 0 5 10 15 20

GaussianTopHat

Figure 4-10: For craters with same depth = 220 nm and near threshold fluence, rim height is lower for top-hat crater than for the Gaussian crater. top-hat crater: f = 50 mm, E = 50 μJ,

depth = 220 nm, width = 16 μm. Gaussian crater: f= 50 mm, E = 20 μJ, depth = 220 nm, width = 12.4 μm. The x-axis is in μm, y-axis is in nm. The data-points are indicated by arrows in

Figure 4-9.

TOP-HAT GAUSSIAN

Figure 4-11: AFM images of the top-hat and Gaussian craters compared in Figure 4-10. The top-hat craters are always circular and have a uniform rim as compared to the Gaussian craters

78

Figure 4-10 compares the AFM cross-sections of a typical case of a top-hat and

a Gaussian crater with similar crater depths, implying similar laser fluences. The rim

height is seen to be lower for the top-hat crater. The AFM images of the two craters

are again shown in Figure 4-11.

In this project, a tight circular aperture is used to truncating the Gaussian

beam to create the top-hat beam profile. Figures 16 till 19 below give a comparison

between typical trends for craters ablated by the truncated and untruncated

Gaussian beam. The difference in trends for the crater width and for the rim

height/crater depth variation as a function of the axial displacement proves that

reshaping the spatial beam profile does affect the crater morphology. This is also

validated by the crater width calculations for the truncated Gaussian beam, which

shows that the crater width at the focal plane corresponds to that for an Airy disk

beam profile.

0

2

4

6

8

10

12

14

16

18

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


NA 0.08, 8 microJ G

NA 0.08, 20 microJ, G

NA 0.28, 15.2 microJ TH


Cra

ter

Wid

th [

⎝m]

Cra

ter

Wid

th [

μm]

Figure 4-6: Variation in crater width with distance from focal plane. The x-axis is normalized by the Rayleigh range. The trend is different for the Gaussian and top-hat craters.

79

0

100

200

300

400

500

600

700

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Cra

ter

Dep

th [

nm

]

NA 0.08, 8 microJ G




Figure 4-12: Variation in crater depth with distance from focal plane. The x-axis is normalized by the Rayleigh range. In case of both the Gaussian and the top-hat beam profiles, the crater depth decreases with increasing distance from the focal plane. In all cases shown, beam spot

size ~ 6 micron.

0

20

40

60

80

100

120

140

160

180

200

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Rim

Hei

ght

[nm

]

NA 0.08, 8 microJ G




Figure 4-13: Rim height decreases for both Gaussian and top-hat beam profiles as we move away from the focal plane. The x-axis is normalized by the Rayleigh range. In all cases shown,

beam spot size ~ 6 micron.

80

0.00

0.10

0.20

0.30

0.40

0.50

0.60

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Rim

Hei

ght/

Cra

ter

Dep

th

NA 0.08, 8 microJ G




Figure 4-14: rim height/crater depth Ratio decreases as the beam profile changes from airy disk to top-hat. The x-axis is normalized by the Rayleigh range. It behaves in the inverse

fashion when the beam profile stays Gaussian all through. This shows that beam shaping is an effective method for controlling the crater rim height development. In all cases, spot size ~ 6

μm, depth ~ 700 μm

Hence Figure 4-9 and Figure 4-14 show that truncating the Gaussian beam

with a sharp aperture to create a top-hat does affect the crater morphology, and the

rim height/crater depth for the top-hat profile is lower than for the Gaussian profile,

as originally expected. As a conclusion, the beam shaping does indeed affect the rim

formation process during ablation with femtosecond laser pulses.

81

5 Concluding Remarks

5.1 Summary of Major Results and Conclusions

5.1.1 Experimental Procedure

• Spatial Reshaping of Laser Beam from Gaussian into Top-Hat: By

truncating the incoming femtosecond beam with a very small circular

aperture, we show that we can successfully reshape the Gaussian laser beam

into a top-hat spatial profile. In our case, we use a 3.5 mm diameter aperture

for a 22 mm diameter Gaussian beam. This method is inexpensive and easy

to implement, but is not efficient in terms of energy. Hence this technique

serves as a good method for showing our proof of concept, but is not good to

be used on a commercial scale.

• Improving Laser Beam Shape by Slight Truncation: The laser beam

transverse cross-section and the resulting ablation craters can be made

circular by placing a low truncation ratio circular aperture before the focusing

lens in the beam path. It acts like a crude spatial filter and removes the

higher order Fourier transform components from the beam to a certain

extent. These craters have a homogenously distributed rim, as compared to

the uneven rims of the elliptical craters made by ablation with an untruncated

Gaussian laser pulse. The calculated energy density in the side-lobes of the

Airy disk pattern is expected to be less than 1% of the maximum energy and

thus does not affect the ablation results.

• Effect of Focal Plane Location: We have experimentally validated the fact

that the crater morphology (crater width, depth and rim height) changes

depending on the position of the sample surface relative to the focal plane of

the focusing lens. It is worth noting that the crater rim height, in general,

decreases as the focal plane of the focusing lens moves inside the sample

surface (trend shown in Table 1). This happens probably because the high

fluence in the bulk of the substrate causes breaking of bonds inside, thus

82

compressing the material. This, in turn, causes the crater to sink below the

surface level, without forming a well-defined rim. Hence, for a given

experimental setup, the sample surface can be positioned such that it can

take advantage of this physical phenomenon, thus resulting in reduced crater

rim heights. Also, machining should be avoided with the sample surface

beyond the focal plane, to avoid any beam distortion effects by the

dissociation of air at the focal point.

5.1.2 Experimental analysis

• Rim Height Relation With Crater Size: b/h ∝ 1/D2: The crater rim height

is shown to be a function of the crater width and depth. It is known that the

crater depth is solely dependent on the fluence, while the crater width is a

function of both the fluence and the beam spot size. We measure the

dimensions of the crater and the rim for different combinations of fluence and

spot size. Our experiments indicate that the ratio of the rim height to

the crater depth is inversely proportional to the crater width.

• Affect of the Top-Hat Beam Shape: Comparison of trends between the

craters ablated by the untruncated (Gaussian) and the truncated (top-hat)

beam profiles shows that beam shaping influences the crater morphology

[Table 1].

In case of ablation with the Gaussian pulse profile, the spatial beam

profile remains Gaussian as the sample surface moves away from the focal

plane (in either direction). Although the absolute rim height becomes smaller,

the rim height to crater depth ratio increases, implying that the rim height

decreases more slowly as compared to the decrease in the crater depth.

On the other hand, when working with the truncated laser beam, the

pulse profile transitions from an Airy disk to a top-hat as the sample surface

moves away from the focal plane. As in case of the Gaussian craters, the

crater rim height is highest at the focal plane, and decreases with distance

83

from the focal plane. However, the rim height to crater diameter ratio seems

to be constant in the Rayleigh range and starts to decrease beyond it. This

implies that the rim height and crater depth decrease at the same rate

initially and then the rim height starts decreasing more sharply. Thus the

top-hat results in a lower rim height to crater depth ratio.

• Overall Dependence of Rim Height: The crater rim height is more a

function of the crater dimensions, than of the beam profile. The top-hat beam

profile appears to yield a lower rim, but the reduction is small compared to

the reduction in rim height achieved by increasing the crater diameter. Hence,

craters larger than 30-40 μm are rimless because of their large diameter;

while rim heights of craters smaller than approximately 10 μm may be

reduced by reshaping the beam into a top-hat.

Table 1: Summary of General Trends as a function of Focal Plane Location

Gaussian Top-Hat Crater Width Smallest at focal plane

Widest at focal plane

Crater Depth Deepest at focal plane Deepest at focal plane

Rim Height Highest at focal plane Highest at focal plane

Rim Height/Crater

Depth

Lowest at focal plane Highest at focal plane

Note: the x-axis for all sketches is ‘distance from focal plane’, with the focal plane at the center.

84

5.2 Recommendations for Future Work

The main objective of this project is to understand the reason for the surface

roughness observed while making microchannels in dielectric materials using

femtosecond laser pulses. Previous studies show that the surface roughness is

caused when craters overlap when using multiple laser shots. The rims of the

individual craters diffractively interact with each other leading to periodic surface

features. The dimension of these microfeatures is of the order of the wavelength of

the laser beam.

We have focused entirely on single-shot ablation in this project. The crater

profile is expected to mirror the laser pulse spatial profile. Hence the walls of a

‘Gaussian’ crater should be more slanted than the walls of a ‘top-hat’ crater. This

effect is difficult to identify with single shot ablation craters owing to the small

dimensions involved. However, we expect that when multiple pulses overlap at the

same spot, the effect would get exaggerated and the walls of craters made with, say,

5 laser pulses, will show drastically different morphology depending on the pulse

profile.

The relationship between the crater diameter and the rim height should also

be extended to check if the surface roughness decreases when machining large sized

multishot ablation channels.

The next logical step is, therefore, to compare the effect of multishot ablation

with the Gaussian and the top-hat beam profiles, and with craters or channels of

increasing sizes. This should be done both with multishot craters and with continuous

channels.

85

6 Appendix :

6.1 Appendix A: M2 Measurement Measuring M2 factor:

Real-time beam diagnostic measurements are recorded using the UNIQ TM-7CN CCD camera with Spiricon software, having a pixel array of 1254 x 1148 pixels and a pixel size of ~9.8 μm per pixel. A frame grabber card together with Spiricon LBA 300PC software v3.03 is used for the 2-D intensity distribution analysis of the captured digitized images. These measurements are used to determine the lens focal distance, the laser M2 propagation factor etc.

Detailed specifications on the camera are given at the end of this section. The following measurements are taken:

• Width of the smallest focused spot in x and y directions • Position of the focused spot relative to the focal length of the lens • Beam width at the focal length of lens (might be different from the smallest

spot size) • Divergence angle of the beam beyond focus

Notes:

• The lens is kept fixed and the detector is moved on the rail in the axial direction.

• The measurements were done with two energy calculation settings in the software to validate the calculation

o 86% energy method o Knife-edge method

• The number of ‘illuminated pixels’ was also counted randomly to check the software calculations.

• Barely enough filters were used so that the CCD chip was just below saturation level, for an accurate beam size measurement.

• Absorbing filters were avoided in the experiment because they have non-linear energy absorption and cause the shape of the beam and hence the divergence and size readings to get distorted. Reflecting filters were used instead.

• Ultracal™ (algorithm provided by Spiricon) was used to eliminate background noise, to ensure better readings.

• Minimum size of the beam should be 100 microns, so that enough signal is received by the CCD chip to ensure correct size calculations

• ‘Origin’ software was used for the non-linear curve fitting.

86

Sample Measurements: (Note: this graph is used as an example only)

110 120 130 140 150 160 170 180 1900.10

0.15

0.20

0.25

0.30

0.35

0.40

Data: Energy86_DiameterXModel: user1Weighting: w No weighting Chi^2/DoF = 0.00017R^2 = 0.97785 P1 0.06936 ±0.00276P2 1.21312 ±0.04216P3 147.32917 ±0.63554

Mea

sure

d B

eam

Dia

met

er a

long

x-a

xis

[mm

]

Axial Distance z [mm]

DiameterX

Specifications of the UNIQ CCD (Charge Coupled Device) Camera (model TM-7CN): Imager 1/2" interline transfer CCD Sensor Size 6.4(h) x 4.8(v) mm (4:3 Aspect Ratio) Chip Size 7.95(h) x 6.45(v) mm Cell Size 8.4(h) x 9.8(v) microns Pixel Array Size 768H x 494V (Sensor Size/Cell Size) Output Analog Bit Depth 8-bit camera (Grayscale level 256) (Dynamic range

48 dB) Scanning 525 lines 60Hz Irising Auto Iris LensAcquisition Rate 30 Hz (interlaced video)

0.3 μW/cm2 CW and 3 nJ/cm2 pulsed Saturation Level

87

6.2 Appendix B: Properties of Borosilicate Glass Properties of borosilicate glass are listed below: Chemical composition: 81% SiO2, 13% BB2O3, 2% Al2O3, 4% Na2O Band gap energy: Eb < 4 eV Refractive index: 1.472 Density: 2.23 g/cm3 Abbe Number: 65.7 Coefficient of Linear Expansion: 3.20 Viscosity: ≈103 Pa.s (1500 K) ≈102 Pa.s (2000 K) 1-10 Pa.s (>2500 K) Surface Tension: 0.28 J/m2

Thermal conductivity: 1.25 W/mK (300 K) 1.60 W/mK (600 K) 4.50 W/mK (900 K) 42.0 W/mK (1500 K) Specific Heat: 746 JKg-1K-1 (300 K) 1000 JKg-1K-1 (600 K) 1250 JKg-1K-1 (900 K) 1320 JKg-1K-1 (1500 K) Thermal Diffusivity: 0.75 m2/s (300 K) 0.72 m2/s (600 K) 1.60 m2/s (900 K) 14.3 m2/s (1500 K) Annealing temperature: 560°C Softening temperature: 821°C Working point: 1252°C Melting Temperature: 1500 K Strain point: 510°C

53

6.3 Appendix C: MATLAB Code Listing %CALCULATING VARIATION IN SINGLESHOT ABLATION CRATER DIMENSIONS WITH DISTANCE FROM FOCAL PLANE %fluence2 hold on %Known Parameters from Experiment Setup: w_0 = 4; % initial beam size (radius) in mm lambda = 0.780e-3; %wavelength in mm f = 100; % focal length in mm F_threshold_single = 2.6; % J/cm2 F_threshold_multiple = 1.7; % J/cm2 alpha_inverse = 240; %optical penetration depth in nm E_pulse = 120e-6; % incident laser energy in Joules %Focal Spot Characteristics: % w_1 = f*lambda/(pi*w_0) %focal spot size in mm w_1 = 13.9e-3 %focal spot size [mm], (from spotsize measurements) z_R = pi * w_1^2/lambda %Rayleigh range in mm F_0_peak_0 = (E_pulse*100)/(3.14*w_1^2) % Peak Fluence Joules/cm^2 D_0 = (2*w_1^2*log(F_0_peak_0/F_threshold_single))^0.5 %Crater Width [mm] at Focal Plane h_0 = 240*log(F_0_peak_0/F_threshold_multiple) %Crater Depth [nm] at Focal Plane %Variation with axial Location: z = -2:0.1:2; %axial distance in mm w_z = w_1*(1+(z./z_R).^2).^0.5; %beam size at z axial location, in mm % plot(z/z_R,w_z*1000,'-r') % title('Fluence'); ylabel('Axial Location z, [mm]'); % hold on F_0_peak_z = (E_pulse*100)./(3.14*w_z.^2); %Peak Fluence [Joules/cm^2] % plot(z/z_R,F_0_peak_z,'.b') D = (2*w_z.^2.*log(F_0_peak_z./F_threshold_single)).^0.5; %Crater Size [mm] plot(z/z_R,D*1000,'.c') h_z = alpha_inverse*log(F_0_peak_z./F_threshold_multiple); %Crater Depth in nm % plot(z/z_R,h_z,'.r') % I_0 = 2*P/(pi*w_0^2); % I(r,z) = I_0*(w_0/w_z)^2*exp(-2*r^2/w_z^2); Calculation of 3-D variation % of intensity with axial and radial distance % L = legend('Beam Spot Size [micron]','Fluence [J/cm^2]','Crater Size % [micron]','Crater Depth/100 [nm]'); % set(L, 'FontSize', 7) title('Gaussian Beam Profile, f = 100 mm'); xlabel('Distance from Focal Plane [normalized by Rayleigh range]');

89

6.4 Appendix D: Ablation With Gaussian Beam Profile Trends Seen with Gaussian Beam Ablation:

1) f = 50 mm, w0 = 6.2 μm:

Crater Width (Gaussian, f = 50 mm)

0

5

10

15

20

25

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5Relative Axial Location [normalized by Rayleigh Range]

Cra

ter

Wid

th [

μm

]

8 microJ10 microJ20 microJ30 microJ40 microJ

Crater Depth (Gaussian)

0

100

200

300

400

500

600

700

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

Relative Axial Location [normalized with Rayleigh Range]

Cra

ter

Dep

th [

nm

]

8 microJ, 6.5 J/cm210 microJ, 8.2 J/cm220 microJ, 16.4 J/cm230 microJ, 24.7 J/cm240 microJ, 32.9 J/cm2

90

0

20

40

60

80

100

120

140

160

180

200

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

Distance from Focal Plane [normalized with Rayleigh Range]

Cra

ter

Rim

Hei

ght

[nm

]

8 microJ, 6.5 J/cm210 microJ, 8.2 J/cm220 microJ, 16.4 J/cm230 microJ, 24.7 J/cm240 microJ, 32.9 J/cm2

Rim Height/Crater Depth (Gaussian)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5Relative Axial Location [normalized by Rayleigh Range]

Rim

Hei

ght/

Cra

ter

Dep

th

8 microJ10 microJ20 microJ30 microJ40 microJ

91

2) f = 100 mm, w0 = 13.9 μm:

0

5

10

15

20

25

30

35

40

-1.50 -1.00 -0.50 0.00 0.50 1.00 1.50


Cra

ter

Wid

th [

mm

]80 microJ120 microJ

0

50

100

150

200

250

300

350

400

450

500

-1.50 -1.00 -0.50 0.00 0.50 1.00 1.50


Cra

ter

Dep

th [

nm

]

80 microJ120 microJ

92

0

10

20

30

40

50

60

70

80

90

-1.50 -1.00 -0.50 0.00 0.50 1.00 1.50


Rim

Hei

gh

t [n

m]

80 microJ120 microJ

Rim Height/Crater Depth (Gaussian, f=100mm)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Relative Axial Location [normalized with Rayleigh Range]

Rim

Hei

ght/

Cra

ter

Dep

th

80 microJ120 microJ

93

3) f = 250 mm, w0 = 33.4 μm:

Crater Width (f = 250 mm, Gaussian)

0

20

40

60

80

100

120

-10000 -5000 0 5000 10000 15000Distance from Focal Plane [÷m]

Cra

ter

Wid

th [

÷m

]

103 microJ500 microJ1065 microJ

Crater Depth (Gaussian, f = 250 mm)

0

50

100

150

200

250

300

350

400450

500

-3500 -2500 -1500 -500 500 1500 2500 3500

Distance from Focal Plane [mm]

Cra

ter

Dep

th [

nm]

103 microJ

500 microJ

1065 microJ

53

Rim Height (Gaussian, f = 250 mm)

0

5

10

15

20

25

30

35

40

45

-3500

-3000

-2500

-2000

-1500

-1000

-500 0 500 1000 1500 2000 2500 3000 3500


Rim

Hei

ght

[nm

]

103 microJ500 microJ

Rim Height/Crater Depth (Gaussian, f = 250 mm)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

-3500 -2500 -1500 -500 500 1500 2500 3500


Rim

Hei

ght/

Cra

ter

Dep

th

103 microJ500 microJ

95

6.5 Appendix E: Ablation With Top-Hat Beam Profile Trends seen with ablation with top-hat beam profile 1) 10X Objective, NA = 0.28, w0 = 4.8 μm:

0

1

2

3

4

5

6

7

8

9

10

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

Distance from Focal Plane [normalized by Rayleigh Range]

Cra

ter

Wid

th [

μm

]


0

100

200

300

400

500

600

700

800

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Cra

ter

Dep

th [

nm

]


96

0

20

40

60

80

100

120

140

160

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Rim

Hei

ght

[nm

]


0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Rim

Hei

ght/

Cra

ter

Dep

th


97

2) f = 50 mm, NA = 0.06, w0 = 4.8 μm, E = 50, 80, 296, 409 μJ

0

5

10

15

20

25

30

35

40

-3000 -2000 -1000 0 1000 2000 3000

Distance from Focal Plane [μm]

Cra

ter

Wid

th [

μm

]


z

0

100

200

300

400

500

600

700

800

-3500 -2500 -1500 -500 500 1500 2500 3500Distance from Focal Plane [μm]

Cra

ter

Dep

th [

nm

]


53

0

10

20

30

40

50

60

70

-3000 -2000 -1000 0 1000 2000 3000Distance from Focal Plane [μm]

Rim

Hei

ght

[nm

]50 microJ80 microJ296 microJ

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

-3000 -2000 -1000 0 1000 2000 3000

Distance from Focal Plane [μm]

Rim

Hei

ght/

Cra

ter

Dep

th

50 microJ80 microJ296 microJ

99

7 References:

[1] E. N. Glezer, M. Milosavljevic, L. Huang, R. J. Finlay, T.-H. Her, J. P. Callan, and E. Mazur, Three-dimensional optical storage inside transparent materials, Opt. Lett. 21(24) (1996).

[2] A. Marcinkevicius, S. Juodkazis, M. Watanabe, M. Miwa, S. Matsuo, H. Misawa, and J. Nishii, Femtosecond laser-assisted three-dimensional microfabrication in silica, Opt. Lett. 26, 277 (2001).

[3] Yan Li, Kazuyoshi Itoh, Wataru Watanabe, Kazuhiro Yamada, and Daisuke Kuroda, Three-dimensional hole drilling of silica glass from the rear surface with femtosecond laser pulses, Opt. Lett. 26(23), 1912 (2001).

[4] S. Matsuo, A. Marcinkevicius, R. Waki, K. Yamasaki, M. Watanabe, V. Mizeikis, S. Juodkazis, and H. Misawa, Three-dimensional modification of transparent materials by focused femtosecond pulses, Symposium on "Microjoining and Assembly Technology in Electronics" 8th, 489 (2002).

[5] K. Yamasaki, S. Juodkazis, S. Matsuo, H. Misawa, Three-dimensional micro-channels in polymers: one-step fabrication, Appl. Phys. A 77(3-4), 371 (2003).

[6] M. Masuda, K. Sugioka, Y. Cheng, N. Aoki, M. Kawachi, K. Shihoyama, K. Toyoda, H. Helvajian, and K. Midorikawa, 3-D microstructuring inside photosensitive glass by femtosecond laser excitation, Appl. Phys. A 76 857 (2003).

[7] Y. Cheng, K. Sugioka, and K. Midorikawa, Microfluidic laser embedded in glass by three-dimensional femtosecond laser microprocessing, Opt. Lett. 29(17), 2007 (2004).

[8] A. Vogel, J. Noack, G. Huttman, and G. Paltauf, Mechanisms of Femtosecond Laser Nanosurgery of Cells and Tissues, Appl. Phys. B Invited Paper (2005).

[9] N. Shen, D. Datta, C. B. Schaffe, P. LeDuc, D. E. Ingber, and E. Mazur, Ablation of Cytoskeletal filaments and Mitochondria in Live Cells using a Femtosecond Laser Nanoscissor, Mol. & Cell Bio. 2(1), 17 (2005).

[10] I. Maxwell, S. Chung, E. Mazur, Nanoprocessing of Subcellular Targets using Femtosecond Laser Pulses, Med. Laser Appl. 20, 193 (2005).

[11] Heisterkamp, I. Z. Maxwell, E. Mazur, J. M. Underwood, J. A. Nickerson, S. Kumar, and D. E. Ingber, Pulse Energy Dependence of Subcellular Dissection by Femtosecond Laser Pulses, Opt. Exp. 13(10), 3690 (2005).

[12] M. F. Yanik, H. Cinar, H. N. Cinar, A. D. Chisholm, Y. Jin, and A. Ben-Yakar, Functional Regeneration After Laser Axotomy, Nature 432, 822 (2004).

[13] G. Grillon, P. Balcou, J. P. Chambaret, D. Hulin, J. Martino, S. Moustaizis, L. Notebaert, M. Pittman, T. Pussieux, A. Rousse, J. P. Rousseau, S. Sebban, O. Sublemontier, and M. Schmidt, Deuterium-Deuterium Fusion Dynamics in Low-Density Molecular-Cluster Jets Irradiated by Intense Ultrafast Laser Pulses, Phys. Rev. Lett. 89(6), 065005 (2002).

53

[14] T. Baumert, B. Biihler, M. Grosser, R. Tbalweiser, V. Weiss, E. Wiedenmann, and G. Cerber, Femtosecond Time-Resolved Wave Packet Motion in Molecular Multiphoton Ionization and Fragmentation, J. Phys. Chem. 95, 8103 (1991).

[15] A. Ben-Yakar, R.L. Byer, J. Ashmore, M. Shen, E. Mazur, and H.A. Stone, Morphology of femtosecond-laser-ablated borosilicate glass surfaces, Appl. Phys. Lett. 83, 3030 (2003).

[16] C.B. Schaffer, A. Brodeur, and E. Mazur, Laser-induced breakdown and damage in bulk transparent materials induced by tightly focused femtosecond laser pulses, Meas. Sci. and Tech. 12, 1784 (2001).

[17] L.V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1945 (1964) (Engl. transl. Sov. Phys.–JETP 20, 1307 (1965))

[18] N. Bloembergen, Laser-induced electric breakdown in solids, IEEE J. Quantum Electron. 10(3), 375 (1974)

[19] R.W Boyd, Nonlinear Optics (Boston: Academic Press, 1992), 1st ed.

[20] M. Gupta, Handbook of Photonics (CRC Press 1996).

[21] A.L. Gaeta, Catastrophic Collapse of Ultrashort Pulses, Phy. Rev. Lett. 84(16), 3582 (2000).

[22] T. Yau, C. Lee, and J. Wang, Uncollapsed self-focusing of femtosecond pulses in dielectric media due to the saturation of nonlinear refractive index, CLEO (2000).

[23] D. Ashkenasi, G. Müller, A. Rosenfeld, R. Stoian, I.V. Hertel, N.M. Bulgakova, E.E.B. Campbell, Fundamentals and advantages of ultrafast micro-structuring of transparent materials, Appl. Phys. A 77, 223 (2003)

[24] M. D. Perry, B.C. Stuart, P.S Banks, M.D. Feit, V. Yanovsky, and A.M Rubenchik, Ultrashort Pulse Laser Machining of Dielectric Materials, J Appl Phy 85(9), 6803 (1999).

[25] A. Ben-Yakar, A. Harkin, J. Ashmore, M. Shen, E. Mazur, R.L. Byer, and H.A. Stone, Thermal and Fluid Process of a Thin Melt Zone during Femtosecond Laser Ablation of Glass, Proc. SPIE 4977, 335 (2003).

[26] A. Ben-Yakar, and R.L. Byer, Femtosecond Laser Micromachining of Borosilicate Glass for Microfluidic Applications, to be published.

[27] R. Stoian, M. Boyle, A. Thoss, A. Rosenfeld, G. Korn, and I. V. Hertel, and E. E. B. Campbell, Laser ablation of dielectrics with temporally shaped femtosecond pulses, Appl. Phy. Lett. 80(3), 353 (2002).

[28] T.D Bennett and L Lei, Modeling laser texturing of silicate glass, J Appl Phy 85 (1), 153 (1999)

[29] D. Ashkenasi, A. Rosenfeld, H. Varel, M Wahmer, and E.E.B. Campbell, Laser Processing of Sapphire with Picosecond and Sub-Picosecond Pulses, Appl. Surf. Sci. 120, 65 (1997).

[30] T.D Bennett, D.J Krajnovich, L Lei, and D Wan, Mechanism of topography formation during CO2 laser texturing of silicate glasses, J Appl Phy 84(5), 2897 (1998).

101

[31] J. Sun and J. P. Longtin, Effects of a gas medium on ultrafast laser beam delivery and materials processing, J. Opt. Soc. Am. B 21(5), 1081 (2004).

[32] A.E. Siegman, Lasers (University Science Books, 1986, Chapter 17, ‘Physical Properties of Gaussian Beams’)

[33] A.E Siegman, How to (maybe) measure laser beam quality, OSA TOPS Vol 17, Diode Pumped Solid State Lasers: Applications and Issues, Mark W. Dowley (ed.) (1998)

[34] M.W Sasnett and T.F Johnston, Jr., Beam Characterization and measurement of propagation attributes, SPIE Laser Beam diagnostics 1414, 21 (1991)

[35] D.M Karnakis, J Fieret, P.T Rumsby, and M.C Gower, Microhole drilling using reshaped pulsed Gaussian laser beams, Exitech Co. Oxford, UK.

[36] J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

[37] http://www.oxfordlasers.com/micromachining/pdfs/papertophat.pdf

[38] K. Kanzler, Transformation of a gaussian laser beam to an Airy pattern for use in focal plane intensity shaping using diffractive optics, SPIE Con. Laser Beam Shaping II , August 2nd presented in San Diego CA Con # 4443-09.

[39] A. Ben-Yakar, and R.L. Byer, Femtosecond laser ablation properties of borosilicate glass, Jour. Appl. Phy. 96, 5316 (2004).

[40] H. T. Yura, and T. S. Rose, Gaussian Beam Transfer through hard-aperture optics, Appl. Optics 34(30), 6826 (1995).

102

8 Vita

Priti Duggal was born in Goslar, W. Germany on February 16, 1980, the elder

of two children, to Ashwani Duggal and Mridula Sood. She was home-schooled in

Batala (Punjab, India) during the critical high school years. She graduated from the

Indian Institute of Technology, (IIT) in Delhi, in August 2001, where she received a

Bachelor’s degree in Mechanical Engineering. This was followed by a two year work

stint with the GE Global Research Center in Bangalore, India, where she developed

detailed know-how in the area of gas turbines and information technology. Since

August 2003 she has been pursuing her Master of Science degree in Engineering at

the University of Texas at Austin.

Permanent Address: 22, Urban Estate,

Batala, Punjab – 143505

India

This thesis was typed by the author.

103

Copyright by Priti Duggal 2006 · Priti Duggal, MSE The University of Texas at Austin, 2006...

Documents

Transcript of Copyright by Priti Duggal 2006 · Priti Duggal, MSE The University of Texas at Austin, 2006...